I think the left in Britain is very weak - certainly weaker than at any time I can remember and probably weaker than at any time since the rise of the Labour Party, perhaps weaker than at any time in the 20th Century.
If by 'the left' you mean the various would-be revolutionary grouplets (Trot, Tanky, Narchist etc) then I think the Social Workers, who are the largest of the little groups, may well have the most influence, though that's very little influence. I'm not sure they are much more important than the Socialist Party (I mean the Millies, as they used to be, not the Speegy Geebees), though. If I talked Leftese rather than English, I'd probably suggest that there is no qualitative difference in the level of influence between the two groups.
Honestly, Resistance, talk to young people about politics or just listen to them. Many are interested in some big issues - for example, our rulers' military adventure in Afghanistan, the state of the labour market, who deserves or doesn't deserve what income for what, immigration, climate, crime and policing and so on and so on - but the idea of socialism means nothing to most young people. This is a new situation in my lifetime. When I was young, of course many people were opposed to any notion of socialism and people had different accounts of what it meant and whether it was a good idea or a practical idea or not etc, but at least there was some notion that people argued about. Now, there's just a blank. As far as I can see, it means nothing to the bulk of the younger generation. Nothing!