It would help tremendously if your profile gave us some idea of your aviation knowledge/ experience.
You said it was overcast at 800-1000ft... and then a 4-engined jet appeared. Except in dire mergency, in which case it would have been national news, there is no way in this world that such an aircraft is going to fly over Trafalgar Square below 1000ft.
London City Airport is about 8 miles east of Trafalgar Square. I believe they have been landing to the east the last few days so it would be on it's approach. I stand to be corrected but the lowest it would be in that position would be 2000 ft.
It is acknowledged by aviation professionals that normal humans cannot accurately determine the height of an aeroplane or helicopter. The only people who can estimate cloud height with any degree of accuracy are professional observers. When I worked at Heathrow, rarely a day would pass without some member of the public ringing to say they had seen two aircraft "very close together". Pity they had nothing better to do!
If there had been a "close liaison" over Trafalgar Square I am certain that you would not be the only person in the world to know about it.