> and either build a payment processor

Risk, time, complexity, mismatched skill-sets... "getting a new thing built" didn't work so well with (for example) Fujitsu and the Post Office, or the billions spent to little or no avail on NHS digitalisation. Seems to be a case of "damned if you do, damned if you don't".

> use an existing UK company

Are there established UK-based payment processors with equivalent abilities?