You do know that actual political scientists don't use left vs right to describe parties. They use terms like libertarian, socialist, etc. They do that because left vs right change from place to place and time to time. From the POV of the US, Labour are communists. In France perhaps they are center or center left or even center right. Even the things you call left vs right don't remain consistent. There are policies in the 50s which were considered left but now would be right and visa-versa.

PS You have be to be pretty extreme to think the Labour party isn't "left" enough for you. As in, I'm not sure what else they could do to appease the far left in practice without sever negative consequences for the UK.