This is a very good question, and one I had to really look into the answer for. Begin, prior to his election as Prime Minister, was the leader of the "Herut" party, ideological predecessor to Likud in many ways and the successor to Irgun in many others. Even so, he was banned from entering the UK during the 1950s, as the head of a former terrorist group, in their words. Indeed, in the 1950s when his lawyer asked if a visa would be available for a visit to the UK, he was refused after a Foreign Office official wrote to the Home Office, saying:

a visit by him would not do anything to improve our relations with the present moderate government of Israel

The MI5 file noted their assertion that he was:

an extreme nationalist and chauvinist right-wing [sic] and is well-known as the former leader of the notorious terrorist organisation Irgun Zvei Leumi

By the 1970s, this was no longer considered an issue. In 1971, a Home Office note affirmed that Begin was no longer viewed as a security threat.

Begin, by the 1970s, was still no friend of the UK. Even so, he did go to some lengths to attempt to repair some relations with the UK, despite having a very large grudge against them. There are news stories available online showing that he visited the UK almost as soon as he was elected, in December 1977 (he was elected in June). Even so, the consensus is that the Foreign Office was still not happy about his election, and even less happy about the prospect of a visit...but there were not really public incidents, and his visits went off without a hitch. This was made easier by the fact that he and Sadat were developing a working relationship already towards an idea of peace, as seen in Sadat's speech to the Knesset in November 1977. The British government did not want to be on the sidelines, particularly when the US and Soviet Union came together on a statement in October 1977 about a peace process for the Arab-Israeli conference, and so the British government actually invited Begin to visit itself.

In short, the reaction was very muted, though internally there was turmoil. But it definitely got easier over time, because of the moves towards peace, and after around 20 years, the UK essentially stopped judging Begin to be a security risk at all. This type of approach can be seen similarly in the approach of other European countries to the PLO, in that once the group became more political and less involved in direct violence, it became acceptable (and even positive) to host its leaders in the name of peace.