Are private jets allowed to land at London Heathrow?
The answer appears to be "yes", but unless you're transferring directly from the private jet to/from an international flight in/out of Heathrow, it's a poor choice. Fees are high and delays are common.

With no fewer than 13 other airports to choose from, chances are that one of the others will be a better choice. Luton and Farnborough are the most popular choices for private jets.

Reference:

PrivateFly: Inside London Airports - Private Jet &amp; Helicopter charter