It's all down to regulation. If you go through an intermediatory like Transferwise the exchange can't tell the original source so they fail the KYC test. I've traded Futures with brokers in the US for many years and they will not accept any wire unless it's come directly from a bank account with the same name as the brokerage account. Crypto exchanges are coming under more scrutiny and need to adopt the same practices. What I do is buy on Localbitcoins and the transfer that BTC to the exchanges to trade with.
There is a UK exchange called Coinfloor, I don't know much about them but there is a minimum deposit of £1000 with £5 fee.
https://coinfloor.co.uk/feesUnfortunately, even though they're UK based, Coinfloor still bounce all their payments through Poland.
Ah, that's worth knowing. Probably no UK bank able to deal with them. Regulations here are far more stringent than most of the world, even the US.
The only way around it I can think of is if you know someone in the US you trust, with an exchange account. Send the money to them with Transferwise that and get them to buy the coin and send to you.