I think if you want to just copying existing shirts at a low cost would not be worth it to send this type of commission to an Asian operation?
I say this all the time, the reason to choose a bespoke shirtmaker is for their ability to fit your body and Cut therefore a great pattern.
Regarding shirting in London, I have only come across Joel fabric in Edgware Road, just outside the Bakerloo Underground station. They have the Sic Tess books to order cuts from and some rolls in stock. Otherwise, you would be surprised that most shirtmakers in Jermyn streets will also sell fabrics to individuals (mostly from Albini group brands and Acorn; Acorn can be also bough directly from their website).