I am toying with the idea of doing a London based unit using the Duke of Westminster as a financier/commander. A staunch Royalist and friends with the Royal Family.
A real WWI unit was the Queen's Westminster Rifles (an ancestor to my old Army Regt by the way). I was thinking of using early WWI figures and paint them in Rifles Green rather than standard British Khaki. Have found a rather nice commemorative flag which I intend to base the unit flag on:

1st Batt Queens'Westminster Rifles
The current Duke is a cavalryman, and there was in existence the Westminster Dragoons, so an excuse for a few cavalry figs.
Finally, I have discovered that during WWI the Duke of Westminster bought the Rolls Royce Armoured Cars and Tenders used in the desert with Lawrence (the current Duke is currently restoring a Rolls Royce A/C), so an excuse for some A/Cs too!
I quite like the idea of using the Police to form armed units, so maybe 2nd Batt Queen's Westminster Rifles (City of London Police)
Artillery could be supplied by the Honourable Artillery Company.
May take a while to put it all together, but we shall see.