The UK is outside the Schengen area, and it's many years since I last arrived at HAM from outside Schengen... so I'm afraid I can't help you.

I've found that the people at HAM are pretty good at answering emails, so your best bet might to email them (FHG-at-ham.airport.de), explain that you are transferring between non-Schengen flights at Terminal 1, and ask them if you need to go through passport control. There is also a phone number - +49 40 5075 – 1111. As they're publishing this number on the English "Contact us" page I think one can assume that they can handle calls in English.