If money is tight then LHR is worth considering. You would struggle to find a half-decent central hotel for <£100 compared to £45-60 at the airport Sheratons. The rooms at LHR are pretty similar, public areas/lounge better at the Skyline. No restaurants worth making a journey to anywhere near. You need to factor in 1.5 hour travel time to central London plus the cost of an all zone Travelcard (off-peak is cheaper at £8.50 but only valid after 09.30 and all day at the weekend - you can start earlier from the hotel as the local bus to LHR tube station is in the free flow area). Remember you would probably end up buying a central area Travelcard if you stayed in town for £7.00.

BUT ... if you have points to burn at Hyatt Churchill you get to stay at a very comfortable right in the middle of town. If this is a first visit to London or you are travelling with someone and want to show them the sights you would be mad to stay at the airport.
One way to keep costs down is to make lunch the main meal - many of the world famous restaurants offer fantastic deals. The Wallace Collection is almost next door to the Hyatt. It has some extraordinary art and it's free.