Local election turnout has been relatively low for a considerable period of time, so it's nothing new, nor is it  viewed in the same way as national elections, rightly or wrongly.Some parish council posts go unfilled/uncontested.

If voter turnout was the same at national elections as it is at local level, its likely it would be a problem.Turnout at national level tends to be in the 60-70% range currently.It's probably fair to say the long term trend appears down from the broad 70-80% of earlier times. It would be very difficult however to write off a very large sudden drop, especially over a relatively short time scale simply as voter apathy.  Very difficult however to see that situation happening , nor is it clear exactly how that would play out if it did, but it would focus attention.

the referendum result was as much a vote against the system and the people who run it as anything else.
I would say that there's something in that, although some might say at 72% or so turnout compared with 66% at the 15 election that the active disillusioned are not quite as numerous as some might think, or alternatively they didn't see it as significantly more different/more important than national elections, assuming a valid comparison