Yes you can. The easiest way to do this is to leave the airport after your inbound flight via the UK Border, and then re-enter T3 later, you don't need to do or say anything to anyone, nor does it affected any checked luggage in the system.

If, having already got airside to T3, you want to leave, then yes, you can also do it relatively easily. Formally you should ask someone in Customer Services to help you, but if you make a clear note of your way into T3 via Flight Connections, and then retrace your steps, you will find a relatively clear way to the UK Border and out again. There aren't any signs, hence the need to memorise the route back, but once you return to Flight Connections it's clear enough how to get to the UK Border.

If you have arrived into LHR via another terminal other than T3 different logic and permutations may apply.