Trying desperately to remember if arrival and departing pax are segregated at MAN T3 - I seem to recall they are, they certainly are now at the other terminals, so it is likely you'd need to either look for a transit route or go back through security. 25 minutes is doable for T3, it's not a huge terminal, but it really depends on whether any of the TATL flights are due off since they seriously mess up security