I can't speak for his specific veto of the UK's entry into the EU, but I have a bit of information on De Gaulle's opinion of and relation with the British government during WW2, which was surprisingly negative considering what they did for him.

The first damage to relations was Operation Catapult, the destruction of the French Fleet at Mers-el-Kebir by the Royal Navy. The French Fleet had mostly turned over to the Vichy government after the fall of France, and it was viewed as enough of a threat in case it was turned over to the Germans or in the event of a declaration of war by Vichy that it was decided that it should be destroyed. The Strasbourg and two or three other destroyers managed to escape, but the rest of the fleet was sunk or damaged and 1,297 French sailors were killed. This meant that very few French sailors and soldiers were willing to join his free french forces, and he was naturally displeased, especially as pride was very important to him.

In late 1942, Allied forces occupied Madagascar to prevent the Japanese from establishing bases there, and he was angered that the allies were planning to negotiate with the Vichy authorities there. Even though the island was turned over to the French after a long guerilla campaign, he was still unhappy that it was not Free French forces that took the island.

De Gaulle was also not informed about the Operation Torch landings until they had begun. Roosevelt had requested that the Free French be kept in the dark (as they had been with most things), but Churchill asked General Ismay to call de Gaulle's Chief of Staff, General Pierre Billotte, to warn him of the invasion just before the troops landed. General Billotte decided not to wake de Gaulle, so he did not hear the news until after the landings the next morning. He was enraged, and said 'I hope the Vichy people will throw them into the sea, you don't get France by burglary!' Although he later made a broadcast supporting the operation, he was still displeased. Arguably, even if Billotte had woken him before the landings he would still have been unhappy to have been left out.

It is likely that order to the SOE section supporting the French Resistance to avoid the Free French government in London as much as possible due to their antiquated communication systems, which the British knew the Germans had broken, agitated de Gaulle. He had a great determination to unite the French resistance under his command, and the interference of the British without his or his government's consultation or consent frustrated him.

De Gaulle also had disagreements with the Allies over the liberation of France; the Allies, especially the Americans, insisted that they were not installing a Gaullist government in power; they were instead to liberate and occupy until free elections could be organised and held. Roosevelt refused anything other than a military government until this could be done, with special banknotes that de Gaulle abhorred. Even the proposition of AMGOT, an Allied Military Government of Occupied Territories, was a deadly insult to de Gaulle and the French.

Another insult to the already anglophobic and anti-american de Gaulle was his exclusion from the Yalta and Potsdam conferences, especially the former. Even though France would get her zone of occupation in the South-West of Germany, he was still displeased and unhappy at his exclusion from these conferences.

I'm afraid I have little to no knowledge of de Gaulle and the fifth republic after the end of the war, and so maybe someone with more experience in this can elaborate on whether these events had an effect on de Gaulle's opinions and actions post-war.

Sources:

The Second World War - Antony Beevor

D-Day: The Battle for Normandy - Antony Beevor

So caveats first: I am not a historian; I'm approaching this from the politics perspective, but I think the politics answer is neccesarily quite similar to the historian's answer because it's an intensely political situation. I'm also on mobile, so give me a day or so to properly get home, check and provide sources (mods if You'd'be preferred for me to just wait a day I'm sorry for posting now).

Anyway, we need to remember that early efforts at European integration were cast entirely in the shadow of WW2 and to that end they were (markedly) different from contemporary EU politics. In the early days of the EEC (and its predecessor, the ECSC) there was very clearly one leading country: France. It was the only Allied large country in these European communities, and with WW2 just behind, nobody was willing to hand Italy or especially Germany any sort of leadership role out of fear that their past would rear its ugly head again. Additionally, consider (as /u/Spruce_Williams touches on) the intense humiliation suffered by France during the war: the bastion of liberty in Europe had not just fallen to her old enemy, she had been completely occupied in a matter of weeks.

There are other factors, but for brevity these two should serve to underpin understanding the Gaullist mentality in a basic sense: topically, you might call it "make France great again" (yes, really). For Gaullists, the fact that the war in the West had been visibly and publicly won by Anglo-Saxons whilst France had fallen was something that needed to be forgotten and glossed over, quickly.

To that end, then, you can see a pattern of French assertiveness throughout the postwar era in a large way driven by the desire to reignite and further her status as a great power of the world. Postwar France was not ready to accept a bipolar world of two superpowers' blocs, and this is evidenced especially clearly in early European integration. From the outset, de Gaulle (and later Gaullists) would model European communities as intergovernmental (I.e. Business is conducted between national governments, rather than on a supranational level like the EU is in some ways now) to ensure France always had a veto over policies it disliked and, explicitly or implicitly, for the protection of French interests. Even up until the early '80s, European communities were in a real sense designed to enable France to become the centre of Europe and the continent's leading power. Especially in the early days of the ECSC, the agreement effectively increased the market for France's goods whilst providing protection against competition from outside the bloc whilst also granting a level of control over German industry. Security, political and economic concerns all rolled up into one nice package for the citizen who loves la Patrie.

So what we see from this is that France was clearly very unhappy at the idea of a large, traditionally democratic, assertive, free-trading nation joining the EEC: it would dismember to the very core the protectionist, Europeanist vision de Gaulle and his successors had painted. Moreover, you have to appreciate that in the 20th century (and to a lesser extent now) there was a real unease, especially amongst those states more inclined to economic interventionism (as France was/is) about Anglo-Saxon laissez-faire free market capitalism and its ability to undermine the postwar systems other European countries were trying to build. Furthermore, the perceived influence of the US can't be overstated; De Gaulle had already had spats with NATO about basing troops on French soil, and it's in this same line of thought that we get the British rejection, as it would (to De Gaulle) allow the Anglo-Saxon to creep in and derail the European project that had, thus far, kept Germany at bay and under control whilst giving France three decades of nearly uninterrupted moderate to high economic growth.

So did the UK help him during the war? Absolutely - but in doing so it hobbled France on the world stage. The postwar era was a very different time to the war, and De Gaulle desired a strong France at the centre of a strong Europe, with Germany under wraps. Did he trust the UK? Perhaps on some things, but fundamentally he did not (rightly, to be fair) trust the British to always have France's best interests at heart when it came to matters of European policy. It was that which drove British rejection, as until that point, European integration had been a French project that helped France establish its primacy and strength in Europe. The addition of another large, morally "right" (in the war context) economy would unhinge that vision, and entail the reverse of the project until that point: unfavourable policies being forced on France. Whilst it's perhaps a controversial note to end on, it's not hard to see why De Gaulle thought like that - and to some extent, you might say he was right.

Sources (to be amended):
Cole et al (2008) Developments in French Politics 4th Edition

According to Robert and Isabelle Tombs in That Sweet Enemy: Britain and France, it was largely a disagreement on economics. The French vision of the EU was as a continental trading block & customs union. Nations outside the EU would face customs barriers and tariffs. But Britain was still very much head of its empire and as the empire dissolved, it was becoming a trading block still called the British Commonwealth. The British gave tariff and trade advantages to the Commonwealth nations (Canada, Australia, South Africa, etc.) Allowing Britain to join the EU would allow those nations' goods privileged entry into the EU (with Britain as the transit point), defeating what De Gaulle saw as the whole economic rationale of the system.

But then, he also didn't really trust the UK either. Sure, they helped defeat the Nazis, but he did not appreciate the way that Churchill had largely used him as a puppet during WWII, denying him input into the conduct of the war and keeping him in the dark about military plans, even ones of obvious importance to the French. And he was suspicious that if another continental war broke out, they might try to sit it out. Similar suspicions had been common among the French leadership in the run-up to both WWI and WWII.

Last time this question was asked u/124876720 gave a detailed answer.

That might be a good place to start.