Royal Mail's own website says 1-2 days for 1st class and 3+ for 2nd class:
http://www.royalmail....l-delivery-options-uk
However, I know that any mail posted to my parent's house in commuter-belt Surrey, not far from London, when posted 1st class can sometimes take up to three days to be delivered. This is because the local area delivery office in their area (Guildford/Woking) decided to introduce deliveries on alternate days, so 1st class post is taking longer to arrive. No consultation with the public, this was just a decision made by Royal Mail! I'm not sure whether it is still happening but I think it is a bit of a cheek when you are paying for 1st class post and expecting it to arrive within 1-2 days.