His Majesty received in audience the Rt. Hon. Andrew Burnham MP and requested him to form a new Administration. The Rt. Hon Andrew Burnham MP accepted The King’s offer and kissed hands upon his appointment as Prime Minister and First Lord of the Treasury.
That is for footage of parliamentary sessions. Permits are also required for filming on the property. But anyone can stand on the public street and film the building, for any purpose. To suggest otherwise is ridiculous.