You might be out of luck since the only current phone that comes with Android 4 by default is the Galaxy Nexus, and it's hardly "cheap" - you'd struggle to get it much under £450 unlocked. You might be able to get a slightly cheaper Nexus S or Galaxy S II and manually upgrade them to Ice Cream Sandwich but it's a bit messy.
There are some cheap Android 4 phones on the way from the likes of ZTE etc. so if you're prepared to wait you will find one, but for now - no.