I don't know how it works in the UK, but if I were in your situation in the US--needing the cheapest flight for specific dates--I'd first check out the Orlando Airport website, find out what UK airlines (or other airlines that serve the UK) land there, and then do "what if" fake bookings (eliminating every step after they tell you the schedule and fare) on those airlines' websites.

If I didn't have time to do that, I'd ask a travel agent to do it for me. There will be a fee involved, but maybe your time is valuable enough that you will be willing to pay.

The process can be rather time-consuming, which is why I would not ask strangers on an Internet board to do the research for me, but do it myself or ask a travel agent to help me with a more complicated trip.

For example, I think Virgin Atlantic flies from London to Orlando, so you would go to the Virgin Atlantic website, input your dates and number of passengers, and see what you're offered. Repeat for other airlines. Then, when you've narrowed down your choices, phone the airlines to find out what their policies are about disabled travelers.