His chin will be a big factor, especially at HW. I will reserve judgement until he has a couple of pro fights.
Wlad is the best champ of recent years (at least on paper) and before that was Lewis. A chin can be overcome, it just depends how bad it is. I hope Price has got a Lewis like chin where it can be cracked but with the right training and stratey it can be overcome.
He'll escape British level on a Amir Khan basis, good management avoiding the top domestic names, and good match making which'll make him appear to have beaten guys above the top domestic names. His chin is seriously bad though, he was going down everytime he got hit with the big padded gloves and head guards. Goodness knows what'll happen with the head guard of and 10's on.
I thought he had gone with Hayemaker and they were going to give prospects and fans good hard fights and not carefuly matched poo poo careers. Hopefully he gets moved along right and gets a Brit crack around his 10th fight or something similar. His amature pedigree should put him further on the track so better opponents than the usual will be needed.
To answer the question...not very far. He could get to challenge for a British title, and I would expect him to fail in that challenge. Winning a British title would be as far as anyone could realistically aim for him. His chin is FAR worse than Lewis', on a par with Hayes and yet he has nothing like Hayes speed or power. Oh and he is not as skilled as Haye and easier to hit too.
Any British heavyweight that wants to go through Britain to get to the world stage will get tested and maybe found out. Williams and Skelton on their day are world contenders. Rogan seems to be of this ilk. Harrison has a decent domestic record. Sprott is a European gatekeeper and Skelton is Euro proven. So to get past that lot in impressive fashion (like a genuine world class fighter should) would lead me to believe they have something about him.