Depends on a lot of things… Like with Halifax or Bank of Scotland accounts, as long as the payment is going to a faster-payment-receiving bank, and it's not going from certain bank accounts (savings accs mainly, some restricted use current accs) and all the systems are working properly (less said about that the better… Though if they're not, it's worth just not sending it because the outages are short) and it's under £500 (because they don't trust it for bigger payments), it'll go faster payments and be there in under 2 hours, normally almost immediate. But if you run into one of those exceptions it breaks, and goes by BACS.
Oh, also some accounts- mainly building societies and former building societies- delay crediting the destination account by up to (er, I think) 2 days.