I had the opportunity to drop by London haberdashery Benson & Clegg, perhaps more well-known for their cufflinks than their shirts. However, I learned they offer a semi-bespoke and MTM shirt service.
Here are the details:
150 GBP per shirt, 3 shirt minimum
40 GBP sample shirt (for a first time customer)
40 GBP optional bespoke pattern
2 week turnaround
I also learned that their shirtmaker is located in the East End of London. B&C make three visits to NYC per year.
Benson & Clegg covert coat
If you're visiting B&C, you might as well visit Budd Shirtmakers. Here's a bit of whimsy a la cravat if you can read the words on the tie.
Budd window display
And Loake's relatively new store in Prince's Arcade: