Counting doesn't take place until Sunday evening, so I don't suppose we will know anything official on turnout until then.
Some local authorities have verified their votes and therefore have published their individual turnouts.
So, for example, turnout in my area - St Albans - is 47%. Not sure how this compares with the 2014 but is a little up on the local elections a few weeks ago (they were about 40% overall).
However reading Politicalbetting.com there is a trend emerging - specifically that turnout positively correlates with remain % vote in the 2016 referendum - in other words the more remain areas have greater turnout than leave areas.
What this really means for the overall result remains, of course, unclear yet.