What 'Drew said really.
People tend to still support one party irrelevant of whether it's local or national. And unless you're a hardcore constant supporter of that party then you'll vote based on your current opinion of the performance of the parties.
So currently any floating voters that voted LibDem or Con during the General Election will probably decide they're shit now and vote for another party.
I voted LibDem at the General last year for various reasons but I went back to voting Labour this time in the locals and will most likely vote Labour in anything over the next few years.