I finally managed to transfer money with Wise (formerly TransferWise) thanks to the help of T212 support.
Because SEPA payments must be in EUR, I went for a local GBP to GBP transaction. But the transaction information from the deposit-screen is for your specific currency and the money will be rejected because the incoming money’s currency does not match the currency of the T212 account!
Solution:
Send GBP to their GBP account:
GB85BARC20199063688283
Account number: 63688283
1 Churchill Place, London E14 5HP, England
BIC: BARCGB22
Sort Code: 201990
Of course this does not solve the fact that I have to do two currency conversions, but at least the rates should be way better than when my bank does it. I assume credit card payment is still the better option for small amounts