Truefitt & Hill seems to be in St James's Street, nearest tube Green Park. That makes it a short walk from the south end of Regent Street, and would take about as long to get there in a taxi :-). St James's Street runs south from Piccadilly about half way between Piccadilly Circus and Green Park, and Truefitt & Hill should be a short way down there, about half way to Pall Mall.
http://www.truefittandhill.co.uk/locations.php