Welcome to FlyerTalk mitch237uk
No need to worry - two hours, 20 minutes is ample time to connect at LHR. When you arrive into LHR, just follow the signs for the Flight Connection Centre. It's a bit of a hike but hopefully the travelators will be working (they don't always appear to be). At the FCC, follow signs for Terminal 4 and catch the transfer bus which will take you over there.
No security checks to get in your way, but plenty of walking is the norm. At a leisurely pace, this shouldn't take you much more than 30-40 minutes.