First you say you want bespoke, then you say you want MTM and then go back to saying bespoke..... which one is it? What is your per shirt budget?
Assuming you do mean bespoke then the issue you are likely to come across is that most london based shirt makers are comparitavely expensive and often have a minimum order of 5 shirts. Obviously there are the very basic MTM options out there but you are limited with the amount of adjustments they make for you - eg havent seen any that allow you to set the wrist size. Alternatively there are travelling shirt makers that come to London periodically who, subject to currency movements, can offer much better value options and most dont have minimum order numbers.