Is there anyone that I can complain to about the length of time it's taking?
Yeah, ICS bank. Tell them you're unhappy and you want a decision one way or the other. If your credit worthiness is good you should have no problem bringing your business elsewhere. Bear in mind also that if they do approve and issue an offer letter you will probably still have to sort out additional life cover, house valuation ,house insurance and meet with your solicitor. That all takes time - I reckon you could be looking at three to four weeks from loan offer to drawdown unless you have most of the above already sorted.