Cash deposits clear immediately Cheques take 3 - 5 days, depending on whom you bank with (the exact times should be on their web site), to be processed. You can speed up the process by asking for the cheque to be rushed through the system (different places use different names for this service) and by paying the appropriate fee.
Normally if you post a cheque at the same time as you deposit a cheque the funds and the payment should arrive at about the same time unless you are really unlucky. Depositing a cheque on the same day as a cheque is presented wont work unless you make special arrangements with the building society.