Apparently there were no survivors on the plane, and the pilot issued a mayday call shortly after takeoff.

Crashed in Broadwater Gardens, a residential area in Farnborough. The pilot reportedly issued a mayday call just after takeoff from Biggin
Hill.
Sky News reported the plane to be a Cessna Citation. The registration of the plane has NOT been confirmed.
ASN

The airport said the plane was a commercial flight en-route to France. It had just taken off when the pilot made an emergency call and asked for
permission to land again.
"Unfortunately it crashed before reaching the airport," said airport chairman Andrew Walters.
A pilot named as John, who was landing another plane at Biggin Hill, heard the mayday call. The Cessna pilot reported "severe engine vibrations", he
said.
He told the BBC: "You could hear the alarms in the cockpit.
"The pilot came back over the radio a second or two later and said 'We're going down, we're going down'.
"The radio stayed live, and as I turned off the runway I looked back and I saw the plane basically drop out of the sky.
"And then the radio went dead and black smoke came up from over the hill."
BBC news
Without anymore information it's hard to say what happened except maybe it lost power and stalled, but thats a guess.
And Kent is in England, near London. If you've heard of Brands Hatch racing circuit, that is in Kent. It's also probably the original Kent, too.