There is a bus service called the Speedlink Coach which runs every half hour between the two airports, and the journey takes about an hour. The fare is £17 and I don't believe BA pays for it (unless you are in First or Club). I used it to get from LGW to LHR back in April and found it quite convenient, clean and efficient.

Your bags should be checked right through [double check the tags when you check in to ensure this] and there would be no need to claim them if you choose to do the LHR flights. They will be automatically transferred by BA to LGW. You will have tobe at the gate at LGW no later than 45-minutes prior to your flight if you leave either airport.

BA suggests only going into London if you have more than a 7-hour connection. So this iswithin that timeframe if you do the early flight directly into LGW, a bit tight if you fly to LHR.

However, if you have little carryon, then flying into LHR a little later means you could take the tube [a day travel card is £2.80 and cover buses and tubes within London for the few hours you're there] or Heathrow Express into London, spend a couple of hours before heading to Victoria Stationto catch the Gatwick Express. In that case, BA certainly would not pay for your transfer between airports.

Hope this is of some help. I can't recall the cost of the Heathrow or Gatwick Express rail services, but I am sure someone will post this information for you. From experience it always takes longer to get between places in London than one would normally anticipate, so if you go into the city, focus on one area and don't expect to get too much done in the 3 or 4 hours you've got.

Have a good trip and have a wee dram in Glasgow for all us FlyerTalkers.