As I understand it you need to make a SEPA payment.
When you withdraw $ it goes to a European Bank who change it to EUROs at the market rate and it is sent to your bank as EUROs and they again change it to £s at the market rate. It is pretty quick and painless but some UK banks (e.g. NAT WEST) stick an extra fee on top for the EURO exchange - greedy bastards!
What happens going the other way I don't know but I suspect you can't send £s but have to buy EUROs and send them to Bitstamp's Bank, they convert them to $s free of charge. They don't mention a commission. I have not attempted this but check with your bank on how to make a SEPA payment.
This is probably the cheapest way, any other sort of international bank transfers are a rip off.
You are, however, subject to normal currency exchange rates.
Nah, I know that I am making a SEPA transaction, but the money still has to be exchanged and the banks make their money not just by charging a fee, but by giving you 'their' exchange rate as opposed to the actual or corporate exchange rate. As explained in the OP, the cheaper methods of sending money abroad don't deal with Bitcoin exchanges.
I am with RBS, they are generally 3.5% over the actual exchange rate, my mate is with HBoS and he gets charged 4.5%!
This was always reflected in the premiums that you would pay on LocalBitcoins, usually around 5-6%, but something has changed. These guys are selling at around 2% or 3% over spot, and that is with LocalBitcoins taking 1% of total transaction for thmeselves, I want to know how they are doing it!? i.e. obviously they have source of Bitcoin at near spot price and as far as I am aware, that means getting GBP into EUR or USD at practically no charge......