Jim, Wise has a bank account in England, so if you use them you can pay from British bank into British bank. Just try with a modest amount first to build your confidence in the system. Here's the link for new UK customers. You save not just on the transfer costs, but also get a better exchange rate through Wise
I am using oanda.com as a reference for the rate of exchange euro versus PH peso. Tuesday last when I made a transfer by Wise the rate of exchange on oanda.com was 60,53 (preview interbank rate +/- 1%. Wise gave me rate of 60,5632 which include their transfer fee. Excluding that fee the rate will be even higher but of course not realistic as without a fee a transfer cannot be completed.
Same for us with UK banks - only problem is the fuss the barstewards make when we want to move a tiny bit of OUR money.