your right 3 32mm would be better.Why doesn't the heating engineer bit surprise me !!!!!
Sounds a good plan to me Daniel, the vent up to outside (dry part) can be reduced to 3" (75-82mm) according to Building Reg Part H but at a push it could be reduced to 2" (50mm) & it would work fine.
Take the opportunity to sort out wastes if you can, I don't like two 40mm into one.
Good luck.
why the dislike of multiple pipes? I appreciate that as far as I am aware it is not catered for in the regs but should function all the same so long as no one tries to convert the loft and plumb a toilet in to the remaining vent. Ridge tile vents do essentially the same thing by changing the profile of the vent but supplying the same free vent area.