About a 99% chance you'd miss the London flight imo as there is no transit route as you have guessed and the security queues at Manchester are usually pretty long.

This came up recently - not sure why the MCTs are set so low as they are unrealistic

You'd be rebooked onto the next available flight as you are on one ticket

http://philatravelgirl.com/connecting_in_manchester_phl-man_airport_/ - seems there is a transit centre at Manchester ! But sounds a fairly lengthy process with buses - based on this person's experiences it would be very tight to make the flight