How do I transfer bitcoins into a United Kingdom bank account? Does anyone know the best way to change bitcoins into pounds (GBP), then do a bank transfer or paypal transfer? I've found some, but they take a week.
The factors that matter for any cash-out decision are:


Where are you located (country)? (you mention UK)
How much are you looking to trade?
What type of cash are you looking to receive? (you mention bank transfer or PayPal)
How soon do you need access to the proceeds?
Is privacy important?


Specifically for cash-out to PayPal, options include:


http://www.FastCash4Bitcoins.com (among the lowest fees, funds not always available though)
http://www.VirWoX.com (BTC --> SLL, SLL --> USD)


BitBargain is probably your best method:


https://bitbargain.co.uk


Or, of course, you have many local cash out methods:


https://localbitcoins.com/postal_code/uk/london/


And there are local traders who will buy your coins:


http://bitcointalk.org/index.php?action=profile;u=65105
http://bitcointalk.org/index.php?topic=130949.0


You might be able to find someone willing to trade over-the-counter (OTC) but you only want to do this with a trusted counterparty.  The #bitcoin-otc marketplace's Web of Trust (WoT) will help as it has a trust history.


http://www.Bitcoin-OTC.com
http://webchat.freenode.net/?channels=#bitcoin-otc-foyer
http://webchat.freenode.net/?channels=#bitcoin-otc-uk  &lt;-- Specific to UK


Here are more cash-out options:


http://en.bitcoin.it/wiki/Selling_bitcoins