Oh, I absolutely agree that a rental is the best option -- I personally would NEVER do an offsite hotel without one, and actually, we always use one onsite as well -- it's just nice to be able to go wherever we want whenever we want without wasting time. (I think the WDW buses are great for getting to the parks, but no so great for getting anywhere else in a timely manner.)
In the OP's situation, presuming that this is not a situation where getting a car is simply not possible for whatever reason, the best bet costwise is probably adding car hire to the existing holiday package. For UK renters, those rates are almost always the best available, as they include full insurance cover. It could always be added for a period less than the full trip, but honestly, if the rate is good from Sanford, it probably would make sense to just keep it the entire time and cancel the airport transfers.
Also, for a UK visitor, 10 days is a rather brief trip -- I personally wouldn't want to spend a huge piece of it standing around waiting for bus transfers in Florida heat.