It will still be hard for Labour to win in the UK, they will have to win seats that they haven't won in decades. Plus, they can't win seats in Scotland which they have always relied on to get into government.
As for the notion that the majority of people sit near the centre, the issue there is that the centre moves. Look at Malcolm Fraser, he would be in the ALP these days and was not considered to be on the left of the Libs at the time. Same goes for Whitlam, who, remember, came from the NSW Right.
It isn't who is in government which matters the most, it is where the agenda sits. The so-called "middle" has been moving quickly to the right for decades, policies which were unthinkable decades ago are now common place.
DS