Heathrow has short term and long term parking areas close to the terminals. However, these are expensive so it is best to follow some simple rules.

Firstly, if you choose short term parking make sure it really is short term. Stay for more than a few hours and the parking costs add significantly to your total bill for the trip. Really not cheap at all.

Secondly, if you are staying for a few days, consider the private heathrow parking companies. They are based outside the airport perimiter, but will shuttle you in on private busses. The cost is typically 40% less than on-airport parking.