The crank arm slips when pressing hard on pedals with Shimano Nexus I have replaced my wheels with a Shimano Nexus 8-speed internal gear hub set but I may have had the problem before the change. When I push down relatively hard on the crank arm for example starting off quickly or riding uphill fast, the crank arm slips with a jolt. Quite often the chain comes off soon after. I can't really see anything as I'm always obviously riding at the time, and the noise can't be located, but it is very irritating and happens in all gears.

Would anyone be able to tell me what this could be?
I'd start with a new chain as a simple maintenance matter - this should have been done when the new rear cog went on anyway.

Then compare how your new chain lies around the front chainring compared to the old one.  It should mesh fairly well over the whole length of contact, not having phased waves of contact and spaces.

Finally, are you positive its the front chainring skipping?  Your feet are on the cranks so it can still be the back, and you feel it through the pedals which makes it seem to be the front.   Get a friend to ride along side, or try riding on a treadmill or rollers... or even use a gopro and a mount to see what's going on.