Worth posting the local, i.e. Durham, result which is now in
http://www.bbc.co.uk/news/uk-politics-21840009
Labour +24
Independent -1
Lib Dems -16
Tories -7
Durham was the only Labour-held council to face election this time (Labour won two others). The Lib Dems have been massacred, losing 64% of their seats, and have lost their position as the second biggest party to independents. I would think independents are mostly on the left (difficult to tell unless one's in your area). UKIP didn't get a single seat (they did field candidates).
The obvious point is this may be an indication of how the vote will go in other Labour-held areas, either locally or nationally; Labour strengthening its hold, the Lib Dems doing very badly. No move to the right at all.
But it's important not to read too much into this. When the general election rolls around people won't remember these council results. They matter a lot to the parties at the time, and it's ideal content for 24-hour news channels, but they will be soon forgotten. The only local elections that will matter in 2015 will be the ones held at the same time as the national election.