Once the buyers have their mortgage and their Solicitor has all the legal information he requires, you will be in a position to exchange contracts on your property sale. Through your Solicitor you will be expected to set a date for completion of the sale and this must be acceptable to your buyer. The completion date is the day legal possession passes to the new owner and you are expected to leave the property.
Wait until funds have cleared into your bank account and then contact the buyer to hand over the keys. Alternatively, you can arrange for your Solicitor to do this for you.