I can't comment on Bevan's popularity although it could've possibly been affected by his decision in 1951 to resign as Minister of Health following the government's decision to introduce a cut in social services which included a cut in NHS funding. Bevan's resignation came just two weeks prior to the Festival of Britain which the British government through the Ramsden Committee and Board of Trade, but from 1945 onwards under the leadership of Herbert Morrison, had been working on since 1943.

The support for a more right wing Labour Party would have been due to the realization that Britain could not maintain its position as the Third World Power and pursue social reforms resulting in the 'New Jerusalem', that had been a manifesto promise in 1945 simultaneously. They had been warned on this subject in 1945 by John Maynard Keynes, who in a report he submitted to the British government forewarned a 'financial Dunkirk', if Britain attempted to do both. The Attlee Government largely avoided this specific part of the report and pursued both and between 1945-51 there were a subsequent six distinct economic crises within Britain including a 30% devaluation of the pound in comparison to the dollar falling from £1=$4.20 to £1=$2.80.

Obviously there were other circumstances in play such as the premature end of the Marshall Plan in Britain (a year before the conintent) and the start of the Korean War and Britain's subsequent rearmament that is said to have been larger than all other European nations combined. So by 1951, especially after Labour's defeat in the elections it was obvious they had to forfeit their commitments to either the welfare state or their global standing. Additionally Labour had promised 5 million new homes in 1945 in the first 10 years of peace but by 1951 due to their commitments of the welfare state, Britain had only built 750,000 by 1953. The Conservatives in 1951 promised a new housing intitative and from 1954 onwards Britain experienced its biggest housing initiative. It was felt that this was one of the main promises that won the Conservatives the 1951 election, so Labour would have wanted to be able to offer the same in order to win the next election. It was ultimately decided to sacrifice commitments to the welfare state in order to maintain their position as the Third World Power something British government officials still believed they possessed in the height of the Suez Canal Crisis in 1956.

Once again though, I am unsure as to Bevan's personal popularity but I hope I have shed some light on why the Labour government would have wanted to shed some of their more left wing policies.