I don’t think anyone in their right mind would consider Blair’s Labour Party “nominally socialist” - particularly for anyone who remembers the Clause 4 debates at conference. Blairism was the moulding of social democratic principles with conservative economics and it was electorally v popular.

Popular on paper ahead of 1997 and with Murdoch on side. Once in power they shed vote share year on year when the reality of what they were (or weren't doing). Also "able to command a majorty under the UK's FPTP system" is not synonymous with "electorally popular"