I looked and both flights and they operate in and out of terminal 5. If this is a connecting flight on one ticket, you don't have to go through immigration. You follow the "flight connections" signs and will get to your next flight. You will have to go through security.
Use the flight connections tool on the Heathrow website and you will see you should have plenty of time. Now, if you buy them as separate tickets, it's a whole different ball game.
The same on return, no immigration at Heathrow but you will go through security.
The previous poster who was going to Glasgow would have had to also go through immigration. But transfer immigration is separate from the main immigration hall.