I use transferwise' borderless account, I believe their fee varies, but I am sure I used TW to transfer less than $10K to EUR for a fee of 0.38%. It now says[0] it's $4.48 to convert 1000$. Changing $1000 to HUF has $4.98 in fees. Both were lower a couple months ago.

Revolut will also allow you to move 5K GBP per month without any fees[1].

[0] https://transferwise.com/gb/borderless/pricing#conversion_fe... [1] https://www.revolut.com/legal/fees/#exchange