Does your phone run an eSIM? Better yet does it run two esims?
Personally I wouldn’t rely on Mint in the UK - I am a Mint customer and have never got the data to work when I am abroad. Your mileage may vary as I am pretty rural in the UK.
If you can run an eSIM, I’d recommend Gigsky or Nomad for data only roaming esims. Both me and my wife have used those when abroad. I don’t know how their cost compares to Mint.
Or if you can run two esims, get yourself a GiffGaff eSIM when you are back. Easily enough data for a £10 top up. This is what I do now.