At this point of course we are all still EU citizens, and we will be until we lose that status, and all the rights it entitles us to, when Brexit finally kicks in. (As an Irish citizen born and living in England of course I retain all three citizenships...)
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The claim that under Thatcher more council houses were built than under Blair is true, but it's misleading. Council house building was reduced steadily throughout Thatcher's years. By the time Major replaced her it had been virtually eliminated in England. Such social housing as continued to be added was through housing associations. When Labour came to power it continued to rely on housing associations to provide social housing and increased significantly the rate at which these were provided.

There was no move back towards council housing during the Blair Brown years. I believe that it was a serious mistake by those Labour governments not to restore the provision of council houses, or at least to ensure that houses sold by councils were replaced by building new ones, or repurchasing existing properties, on a one-for-one basis. But that's the kind of Labour government it was, the kind now called "moderate".

Jeremy Corbyn of course fought consistently against that policy. That was presented as being "hard left", though the policy he advocated was one which had been held in common with Conservatives before Thatcher came along, under such quasi-Marxists as Churchill, Eden, Macmillan, Alec Douglas-Hill and Heath.