I had a check done recently for my job and with that and HR processes it took ages to get everything through - about 2 months although I was already there on agency thankfully so at least I was working through it until I was ok'd to be employed direct. Others who have come straight in had to wait that time until cleared before starting though.
I had to provide loads of information for my check on set forms and providing past addresses for 6 years, employers etc... criminal/credit history confirmations, references, certified photos, all sorts and was well aware I was having the check done and am fairly certain I had to sign the form to consent to it.
Have they not even given a rough timescale? Have you got a formal job offer in writing?