I have had 2 removed, both benign but have bothered me more with age and grew during last pregnancy.
For the 1st my GP referred me to NHS dermatologist as she said that although they don't normally remove it was big and worth asking and they removed it there and then.
Second time I just asked for private referral. Looked up dermatologists at local BMI hospital and asked GP if she would recommend one.
Initial consultation was reassuring as she checked my skin head to toe for any signs of skin cancers (none) then had mole removed a week later.
Took 20 mins ish. Cost a few hundred - incl pathology report which you can't avoid as they want to make sure but a bit annoying as I had no concerns that it wasn't benign.
Ask up front about all the costs as you may get lots of separate bills for initial consultation, consultant's time, hospital charges, path report.
One has left flat White mark as scar which I can't cover entirely by make up, but is better than lump before.
The other one - you'd never know it had been there. I think the difference is more size and location than dr skill.
Oh, and local anaesthetic, minimal bleeding when toddler thumped 1 day later, quick to heal.