Yes, people like Gordon Yao are good at making a fair impression of such things. However avoid the Asian touts near Star Ferry in TST, they will promise you what you want to hear and deliver you a rag. You will easily recognise them, they are the ones who don't shout 'copy watch' at you.
Most Savile Row tailors will look down on MTM as though it had been trodden in on someone's feet. You would be better off-row with the likes of Cad and the Dandy and Graham Browne who should both be within your budget.