Back in 2006 there was a short lived service operated by Wight Airlines..Sandown Isle of Wight to LCY. Three round trips a day using Navajo G-BBNT.
They did a 75 quid day return special, so had to have a go, splendid never been from the IOW to central London so fast, approx. 30 mins, (plus cheaper than a peak time train fare to Waterloo).
Alas only lasted a few months, back to the boat & train!