Yes, you pay more at airports, but you also get a larger pool of cars to choose from and better opening hours. There is nowhere near Heathrow or Stansted airport (there is a Stansted village, population 6000!) which will have anywhere near the choice or opening times.
The only place you can get to by train from Heathrow is central London (Paddington station), and you don't want to pick up a car there.
Where is your first nights stay from Heathrow? I would suggest getting a train there, and picking up a car when you leave that place.
For Stansted, the trains to London go via Bishop's Stortford to London, but there is also an hourly train north to Cambridge, which is an option. I would suggest dropping your car of at the last overnight place before your departure (Cambridge?), and taking the train the following day from there to Stansted.
Note: spelling is Stansted.