From speaking to people both 18-35 and in older age brackets, I've actually found it's the opposite - the younger generation is relatively impassioned about staying (or mostly indifferent but can't really see why we would leave), and older generations are much more on the fence. In fact, I don't know anyone under 35 who is in favour of Brexit. The older generations, however, start talking about their distrust of Europe, of Germany in particular, and seem to have some vestigial jingoistic pride and feel that Britain is still, or at least can be again, a great nation which can manage perfectly well by itself, thank you very much.

(Obviously I've not canvassed everyone in Britain - just about ten or fifteen people I know reasonably well.)