I'm a regular LCY user (I would be, it's a mile from my house !).
It always surprises me how far away people have come from to use the service. Out in Hertfordshire, plenty from Kent, etc. Strangely the No 1 competitor seems to be Stansted. I know the style of service is different but if Mr MD in Cambridge wants to go to Edinburgh he will use Easy at Stansted rather than the further away premium services. I use Cambridge as an example because one of our employees lives there and needs to go sometimes to Jersey or Isle of Man, for which he happily comes to City rather than Gatwick.
I am sure some cannibalisation of Heathrow passengers takes place. Business travel by train to Edinburgh is effectively dead, but it still is considerable to Manchester. The great thing about the train is that you can catch whichever service is convenient in either direction (the railway are throwing this away in standard class with restrictive ticketing, which can only drive passengers to the budget airlines). This is where VLM (Manchester) and Scot (Edinburgh) can score. In order to offer such flexibility you need not only high frequency, but also to have some spare seats on almost all flights. On these two routes I end up changing my return reservation about 50% of the time. I certainly never drive early morning across London for Heathrow flights any more if there is an LCY one.
The BA service from LCY to Paris was, very quietly, withdrawn. Word was it just cannibalised the Heathrow passengers too much, but I think the Air France service from more business-oriented Orly to LCY squeezed them as well.
There is one aspect of a "one airport market" for London that surprises me. I am always amazed at the numbers of passengers, invariably foreign, who are on itineraries that involve transfers between Heathrow and London City. They always have an air of disbelief as the route is explained.