we are booked on an afternoon BA flight from geneva to heathrow. There are 4 flights that morning going this route. Can and will BA put us on the earlier flights even though we may have paid a cheaper fare for the afternoon flight.

Maybe, maybe not.

Technically, if you have paid a lower fare then your ticket will be non-changeable etc so attempting to get it changed beforehand would not be successful. It might be worth a try getting it changed as often even restricted tickets issued in N. America allow some changes for a fee.

If you are connecting through Heathrow from another flight, then you could ask check in staff at your origin airport just to check you through as far as London and once in London you could ask at the BA desks whether they will let you on an earlier flight. Because of time pressures, staff may accept your coupon and let you off on your merry way. They are quite within their rights to deny you an early flight, though.

If you just have a single journey LHR-GVA, then once again you are at the mercy of BA staff at LHR. You could turn up at the airport and see what the response is but be prepared for a long wait as it is still quite likely that you would have to wait for your ticketed flight.

Be aware that many of the flights to GVA from LHR that have a BA number are actually operated by Swiss who go out of Terminal 2 whereas the BA flights TO GVA are from Terminal 4 which could mean a fair amount of trekking at LHR if you turn up on the off-chance of getting your tickets changed.

You are undoubtedly on a non refundable apex fare.With BA, these are "non changeable".Meaning with BA, very literally not changeable in any way shape or form.There will most likely be someone who has experienced the opposite.But officially, no.If you go to ba.com, you can find a reference to "standby fares".But this is a totally different type of fare which offers only standby.But BA doesnt have any of these fares anyway.So I cant offer you a link to anything on the internet so I would advise you to call.Thats what their website advise--call for questions regarding your fare rules.Best of Luck and i hope this helps.

Maybe it's just me, but somehow I tend to have good luck in situations like this. I worked in a customer service-oriented job for many years, and I found it's a lot easier to tell someone "no" over the phone than if they're standing in front of me, asking very politely for a favor. If you really want this, it might be worth going to the airport early and giving it a try. The worst that will happen is they will say no, and you're back where you started. But then again, you might get what you want. Good luck.

We usually arrive at the airport far too early, and once in awhile when we check in they will offer us a seat on an earlier flight; I suppose if they know the seat on the earlier flight will be empty, they would just as soon fill it and have an available seat on a later flight.

Sure if you want to fly standby.
M