In my experience, lastminute.com only ever lists vanilla double occupancy rooms at the Sofitel under its Top Secret Hotels channel.

So, I'd suggest that you're going to rule TSH out on your room occupancy requirement, before you even get to the parking.

I'd be extremely cautious about the Holiday Extras guarantee too; they won't even agree to it when the lower rate actually has less onerous restrictions or more generous inclusions. It must be an identical offer in every respect but price.

Personally, though I do favour the Sofitel when the time and price is right, I'd probably book a deal at the Skyline (or similar) for room and parking, and then get an Uber to T5. My UberX last week was £10 from Bath Road to T5.