Sorry if this is "old news" but I thought I'd post a couple of tips I found when travelling to UK from Switzerland.
1. Last month I arrived 4 hours early for my flight as it was no use going home after meeting in Zurich. I went to the desk to ask if I could transfer to an earlier flight and they quoted me silly money so I tried asking at another desk in T1 and he said the same but if I just present myself at the gate for an earlier flight they may let me on if seats available. NOTE: I was carry-one baggage only. I went to the gate and hey-presto got on the 3pm LHR flight instead of the 6pm LCY. Makes no difference to me as I need to get to Central London anyway. I didn't beg or plead or give them any BS, just asked nicely
2. On my trip last week the flight was overbooked and they were asking for volunteers to catch a later flight at the gate. No problem I said and they gave me a 150CHF voucher in the form of an ATM card + PIN to just get cash as and when you wanted. Had to wait 2.5 hours for next flight but politely asked if I could use the Sky lounge so the girl rang up and got me in there too

Simply walked back through security and spent a very relaxing couple of hours on free gin and tonics..
I met another chap who tries the same thing every time. He registers at the gate as soon as he arrives to volunteer.
Mike