How many private jets land at Heathrow airport per day?
None!
January 2018 movements, source: CAA
Related: Where does an A-lister land when they waft in from paradise? Yes, Luton
To try to explain why this absence of business planes at a large airport, its important to understand that private aviation in Americas and in Europe are not seen the same way.
In Americas private planes are very common, this is not the case in Europe, where you must be lucky to know someone in your neighboring who is a pilot. As a consequence airliners and other planes have separate lives with different fees paid.
For example, I live in Paris: Business planes use Le Bourget aerodrome (the one which hosts the Paris Air Show -- btw nobody here knows what is the Paris Air Show, as everyone calls it Le Salon du Bourget since it exists... --, while airliners use CDG or Orly airports (and now the remote/low cost Beauvais). This is the same in UK.