If you are booked on a through ticket from MSP to MAN, then the higher allowance applies I believe.

However, it sounds like you have separate tickets from MSP-LHR and LHR-MAN. I'm afraid in that case the fact that you had a higher allowance in business class with Icelandair will be irrelevant to them.

How over are you going to be? A couple of kilos may be overlooked, 15kg extra probably won't!

PS - Excess fees starting at £5 per kilo is actually pretty common on domestic flights - look at Jet2, Ryanair, Flybe etc. while BA has a whole new system which may or may not be better depending on your point of view!