We are based in Manchester but come to London often.
Website is www.charlescampbellbespoke.co.uk
They are full bespoke pattern if drafted for you and kept on file. We don't do fittings but im not 100% sure anyone does fittings on shirts.
PS I didn't mean fittings as such. However, some places do prepare a "trial shirt" and then modify, if necessary, when they make the actual shirt. I'm not sure how common that is, however.