It would be hard to dismiss BBC's influence on the format of British television since the BBC (channels 1 and 2) were originally the
only TV channels on British TV. And, as you rightly pointed out, there's always going to be cross-pollination with TV talent as well. However I don't think it pays to look at the BBC as a unique model in the way that you are (ie "The BBC is different from American networks therefore it's the BBC that has uniquely shaped British TV"). I don't consider the fewer episodes per series/season model to be unique to Britain let alone a BBC invention. In America you tend to refer to these runs as "mini-series", but even them aside it's pretty common to have popular shows only run a dozen episodes a season.
I think the differences might be down to writing styles more than anything though. In the UK it's common to only have a 1 or 2 writers behind a popular series (or guest writers who handle individual episodes), where as in America you can have an entire team of writers. I would imagine having more writers might allow for a larger pool of ideas.