There's currently an attractive AA Business Class fare from MAN to various US cities, mostly notably SAT. I don't know if ex-SAT to MAN is also competitively priced, but if so it might explain why the OP is taking this routing rather than flying directly into LHR.

Nonetheless, that's still a difficult thing to sell to an immigration officer, and will raise all sorts of suspicions.

Unfortunately the OP hasn't come back to us to explain how (s)he intends to travel between MAN and LHR - if it's by train or road, I'd imagine that will raise massive concerns. If by air, much less so, and a MAN-LHR-TXL routing probably wouldn't be too far out of the ordinary.

What is somewhat less clear is why an overnight in London would be necessary anyway - the flight would presumably land early morning, leaving plenty of time to reach Berlin the same day even with a LHR connection.

In immigration terms it does very much look more like a visit, however fleeting, than a transit. I'd also be looking at getting a visa.