In what sense were they the county's slots?
it is the capital of the people of England, many of which have business to conduct there, and it is only reasonable that they be provided with a reasonable means of transport for getting to and from there and/or to connect with London's world hub.
The business model is a free market economy so you're going to need the Treasury to subsidise that as well, that's the conversation you need to have. btw a "reasonable means of transport" in this day and age is the train sadly.