No. They used to be, but rebranded in the 90s to New Labour and changed one of their founding principles of seeking common ownership of the means of production, thereby no longer being a leftist party.
https://en.wikipedia.org/wiki/Clause_IV
https://en.wikipedia.org/wiki/New_Labour
They follow what is referred to as the Third Way. Not socialism, but capitalism light. This was established under Tony Blair and Gordon Brown from 1997 to 2010 and has continued under Keir Starmer since 2024.
https://en.wikipedia.org/wiki/Third_Way
https://en.wikipedia.org/wiki/Premiership_of_Keir_Starmer
Starmer’s third way is a bit different from Blair’s. They pretend to be socialist at times, unlike Blair, and have returned to the old name of just Labour instead of New Labour. Some nationalisation has happened, but this is more becuase of necessity and political pragmatism than leftist principles. They’re a duplicitous party, which performs token amounts of progressivism and bigs it up in their marketing while simultaneously taking a conservative stance the majority of the time. Put simply, they’re a right wing party which pretends to be left to gain the public’s support.
Gil Scott-Heron - The Revolution Will Not Be Televised
https://youtu.be/vwSRqaZGsPw