] There's something I've never been able to find a firm answer to, and that is, in what part of the year was the (London) season, and how long was it?

The Season "officially" began in May. The British upper classes were similiar to migrating birds who would flock to London in March or April, flit and float through a whirlwind of balls and other social events, flock to Ascot in June, flock back to London to continue the whirlwind until mid-August and then flock to their country homes for the hunting season onto the Christmas holiday and then as the new year arrived, began to prepare for the new Season to begin the elegant migration cycle all over again.

Below there is a link for an excellent article which offers more detail on the subject.