Labour are a center party. Of course in your rosy Marxist world the only party even remotely left is The Greens
They've been shifting to the centre-right since New Labour. Recall their policies on tuition fees, marketising the NHS, less-than-inflation rises in minimum wage, caps to welfare, and so on.
That political compass website agrees (FWIW), have a look.
http://www.politicalcompass.org/uk2015