It also depends on the timing of your move/where you plan on living. For example, in September/October, University is starting. This is always the time that I've *conveniently* had to move, so there's been a lot of competition for places, (and therefore increased prices).
You may not get the standard american experience where you fill out an application and they approve it and you get to move in....You may find that the flat you went to view at 2:00pm was actually snatched up by the person who viewed it at 1:40pm. We were lucky enough to be the ones who snatched a place up without too much fuss in Nottingham, but had gotten rejected several times in London because of our unluckiness.
I've found that most places will charge around £35 for a credit check. I've also heard of paying either a Security Deposit equal to 6 week's rent (ie: 1.5 months' rent), and/or some other nonrefundable Agency fee in addition to paying your first months rent upfront.
Some student places include bills, but otherwise, you'll be facing bills for Gas (if your place has it), Electricity, Water, and Council Tax. In order to watch TV, you'll need a TV License too, which gives access to the "Free" Channels.