i'd say quite a few do. Barclays and HSBC for example offer SEPA payments.

Say for example you got a bank account at [bank x] in the UK, denominated in GBP. Now you'd ask [bank x] to set up EUR denominated account. Then use transferwise and transfer out of your GBP to transferwise into your EUR account. Then use those EUR to pay and avoid the double bid/offer.

//edit: to clarify: you would send the money to [bitcoinexchange], not transferwise. so it would be in your name.

Hm. Getting out OK. But can't I easily transfer bitcoins? (not cash). So buy into MtGox, shift bitcoins to kraken and sell there for cash? Or is it really hard to get the bitcoins out of MtGox? (I thought the hard thing are cash withdrawals.)

//edit:

ignore the above. So liquidity / uncertainty is really the only driver of prices between exchanges. wow.

When I look at Kraken I see:
EUR/XBT: €492.95713 / 1  and USD/XBT $676.58714 / 1

why is it so far above MtGox for example which is W.Avg: 392.95 € / 1

Data as of 13/02/14, 12:16. Am I missing something obvious?

Looks like you lose 4 points on exchange rate though (GBP > EUR > USD as far as I understand the Unicredit website correctly- unicredit is the bank covering the transfers for bitstamp). And having a USD account in the UK probably also doesn't make sense because SEPA as far as I understand is only for EUR denominated transfers..

//edit: that said, if you create a EUR account in the UK and use transferwise to convert your GBP into EUR you avoid the 2 bid/offers but only pay one. So you end up with about 2 points + whatever transferwise is away from mid-market. Cheaper than the above but still relatively expensive.