If we're going to get pedantic about the definition of lake, it's actually really far from Bassenthwaite. Windermere is a mere, Coniston, Rydal are waters, and there are tarns aplenty.
(Speaking as a local, this is BS to fool pub quizzers, the big ones are lakes or reservoirs, the little ones tarns, medium are waters. I'd call that a tarn personally. It's not the size, it's the situation IMHO. Windermere is only the most popular because that's where the train goes!)