There's a duty of care to look after you until you get to MCO.
Once you're out of the airport at MCO you're on your own. If you've missed a pre-paid transfer then that's what insurance is for.
If you mean that BA are saying you have to pay to get between LHR and LGW, then I believe that's wrong, although the situation is somewhat muddied by the fact it's AA that have cancelled the flight & US carriers have no duty of care responsibility when the weather is bad.
Have you asked about a reroute into Tampa? BA have some space on tomorrow's flight. I believe it's a holiday weekend in the US so flights from the North East to florida are already very busy. Now they've cancelled everything into MCO for tomorrow it's looking even worse...