You can sign the contracts before you get approval, but your solicitor will advise you against it and have you sign a form stating you are aware of the risk first. It’s your decision at the end of the day.
The problem is that if, for any reason, you don't get approval, you are tied into a binding contract for a lot of money. If you then need to pull out, you will lose your deposit.
The best thing to do is to chase your bank to make sure that they have everything they need from you and are working on it. Often, the bank will be waiting for you to sign some form, or provide a document, and won’t tell you until you ask why it’s taking so long. Don’t make them crazy by ringing them every day though!
Unless the Vendors are putting pressure on to send contracts back you should be ok. If it’s a new house, builders solicitors often get impatient for returned contracts more quickly than most…. Your solicitor will tell you if the Vendors are setting a deadline for return of contracts. Then it's time to make friends with your bank manager!