The "left" nowadays in UK are labelled "liberals".

Traditionally, of course, the Liberal Party is to the right of the Labour Party - but these days on a lot of issues it's seen as to the left. (NB "to the left of New Labour" does not mean left-wing!)

The worry for Labour over this isn't going to be people switching to the Tories, it'll be people staying home, or maybe voting Liberal. Or Green. I think it's likely that in the June European Elections the Greens are going to do very well indeed, and the Labour vote will be very badly hit by abstentions. Since it's on a PR system that won't help the Tories much, unlike in a General Election.