I think the SDP (Mark 2) are very keen on Brexit - which might be a barrier for some.
Um, I think that's already happened. If you're looking for a rejoin-the-EU party, I'm not sure any are campaigning on that, are they?
I wouldn't call them left wing.
That's nice. Why, specifically? Being pro-Brexit isn't sufficient, as there I know there are quite a few left-wing anti-EU people... Overall they seem pretty moderate-left on policy overall. Sure they wouldn't be "left" if they were a wing of the Labour party, but nationally, yes.
(Personally I don't think left-vs-right is important at this point - we should be worrying about liberal-vs-illiberal).