We have looked into this recently (after deciding DVC wasnt for us).
Property prices in the Orlando area have risen considerably in the last 3 years and you are looking at around $250-300k + for a decent sized pool home in the "20 mins to Disney" catchement. Be careful when you look for homes, as only certain developments are allowed to be used for short term rentals. You will find some real bargain homes in Orlando, but often these are in residential areas and unable to be used for rentals, so bear that in mind when you look.
To buy a home priced at $250k you will need between £30k and £50,000 in "cash" for your deposit, fees and costs. This was quite a bit more than we anticipated! You need at least a 20% deposit and preferably more than that.
Definately find yourself a good realtor that is used to dealing with Brits. There are several that are easy to find on the net. Find one you are comfortable with.
The main choice you will have is either to buy new from a developer, or a resale. There are pros and cons with each, so weigh up the options. If you buy from a developer, sometimes your home may not be ready for over year, but they do offer lots of incentives like free furniture packages or upgraded appliances for example.
Another option maybe to have a look at some condos or townhouses. These tend to start around $150K, but you also have maintenance fees to take into consideration.
My best advice is to research, research, research! Good luck!