I'm not aware of British influence on HKG prices. The fragrant harbor has a tradition of custom making clothes for white water buffalo for as long as anyone can remember. People are known to travel there expressly to get good clothes. Will prices beat Beijing? I don't know. But I'm confident that the cost performance (ie. quality vs. price) is competitive on a global scale. Certainly a better bet than Tokyo.

For specific tailor recommendations I'd look to the folks on the HKG forum.