I believe that prior to Hitlers Blitzkrieg attack through the Ardennes forest Britain and France believed that the war would be fought in much the same as WW1 so they decided the best way to win would be to fight a defensive war and slowly bleed the German war machine through attrition, using trenches and artillery like they did last time.

To this end most of the french army was stationed on the north west of france on the border with germany where they built the strongest fortifications on the Maginot line, a series of concrete bunkers and trench lines filled with weapons to combat any threat, they were also protected here from the west by the Rhine River. The british arrayed themselves on the northern border of France with belgium where other, weaker fortifications had been built, although it was never the plan for the british to fight there. The original plan was to push north into belgium and occupy positions along the Meuse river where the terrain would better suit them and the germans would be forced to make an opposed river crossing, which is never good.

However the Belgians wouldn't agree to allow French and British troops to occupy their country, they believed that it would be seen by Germany as taking a side and therefore was an act of aggression.

A few days after German forces invaded the netherlands to the north of belgium, German troops were reported to be crossing the Belgian border and pushing south. This sent the British and French into a panic and the British pushed the majority of its army northwest as fast as possible to take the Muese river positions and I believe there was some fighting at this point against Belgian soldiers but that was over quickly as most Belgian troops were fighting on the German border.

If the germans had actually been pushing for the Muese river things might have gone differently but they had no intention of fighting a war of attrition or making a costly river crossing using mostly infantry. The spearhead of their push went south through the Ardennes forest using Tank divisions accompanied by motorised infantry and light artillery drawn by trucks and halftrack in order to encircle the French and British forces as fast as possible and to bypass the most serious fortifications of the Maginot line altogether, both of which they did.

Its worth pointing out here - because there are a lot of memes about how dumb the Maginot line was - that the reasoning behind its construction was that any major assault would have to involve tanks because infantry just did not have the survivability to successfully take an entrenched position, as seen in WW1. The tanks the French and British used in WW1 and the ones they used in 1939 were not as fast or powerful as the ones we see from 1944 and were simply not capable of making the journey through the rough, dense hills of the Ardenne forest, not in the numbers that would be needed to successfully encircle and defeat the British and French in Belgium so it was assumed the German tanks would be incapable of this as well and they would be forced to attack either the Maginot line or the Meuse River. Obviously, this wasnt the case, Germany had been making a lot of improvements to their tanks and, while it was pretty touch and go for a while with tanks getting stuck in the ditches and dykes in the forest or having to be dug out of mud, enough made it through and completely cut off the Allied army and started pushing south, further into france. The Ardennes were fortified however, but primarily against infantry, when the reports first came in that the Germans were pushing through the forest, it was dismissed as a ruse. By the time the British and French took the attack seriously, it was too late and they were already cut off and ended up in a fighting retreat towards the ports in Normandy.

After the Fall of France when the British army was evacuated, the main plan was actually to go around the world and recruit other allies to join the war against Germany, churchill made nunerous diplomatic missions to Russia, America, China and various other places to recruit help and to get them to open up other theatres of war to take the pressure off of Britain and keep the German Navy from attacking Britains supply routes. The British also did opened up other fronts of their own as well, one of which wasbin north africa. Hitler sent Rommel over to attack british and french occupied territories in order to get to egypt and the middle east and take the oil fields there as Hitler believed access to oil would make or break the war effort. He also tried to incite rebellion and make the local population fight against their colonial oppressers. This gave the British the opportunity to hamper german war efforts and deal some serious damage to the German Army, which they did. Rommel failed and was eventually beaten back. This was also around the time that the first real commando harrassment tactics were used in the war. Britain created several forces of commandos whose main aim was to harrass German infrastructure. They fought mostly using night time landings with small boats and raided costal towns and ports, sometimes with the help of local resistance fighters, but they eventually used a lot of different typesn of vehicles and wrapons tl carty out raids. One of the most famous of which is the lofoten island raid where commanos captured key encription documents that would lead to the decoding of Enigma, but there were many other missions in every theatre lf the war, from the arctic circle to the middle east. Many of the volunteers for these groups were actually free french, polish, dutch or danish etc and many of the commando units that were formed by other countries after the war can trace their roots back to soldiers that volunteered to fight for Britain. Another tactic was to arm resistance fighters in europe. Starting with air dropping propaganda and having spies infiltrate different countries, the British would create a resistance network across the continent that could be coordinated from Britain using radio, they would organise with resistance leaders and airdrop supplies and weapons that would allow them to fight back properly and attacl key positions like supply warehouses or airfields.

However all of these tactics were secondary to gaining more allies and opening up new fronts, that was the main plain once Europe fell, all the night raids and resistance bombings in the world wouldn't have won the war if Britain didnt have allies

So essentially the plan was the same as ww1, the changing times and new technology however made that method of warfare mostly obsolete, which the French and British learned the hard way. After that it was to harass and do as much damage as possible whilst calling on every ally nation and colony possible to help us fight, one of the main problems the British faced was that they had a lot of standing troops and a massive population to conscript from, but they spread out over the world and were too far away to be of much help in defending against an invasion, they did enormous amounts, but they couldnt feasibly send a whole army with all the weapons and supplies it needs all the way round the world to Britain itself.

Source for this: WW2 colourized documentary and its associated history