From Natwest website:
Whenever you pay a cheque into your account, we have to collect the payment from the bank of the person or business who wrote the cheque. Normally, in applying the central clearing cycle it takes three working days (including the day the cheque is paid in) for a cheque to be received at the other bank for payment. This is known as 'clearing a cheque'.
Cheques can be returned unpaid, so you should allow at least four working days to elapse before you use money from a cheque paid in. In some cases, because cheques may still come back unpaid after this time, it may take up to five working days for a cheque to clear and postal delays can extend this period further.
So the answer seems to be 3 - 5 working days.