One of the events on the time trial calendar is a 'open' 10 mile time trial at Burton Fleming on 1st September, run by Scarborough Paragon. This is a bit different from normal events: you have to enter in advance (you can't just turn up), and it tends to attract around 50 riders from the surrounding area. It's based at the village hall in Burton Fleming, where there will be refreshments and prize giving afterwards.
To enter, either see Elaine Ward at the 15-mile TT on Wednesday or the 2-up after that, or enter online. You'll need to create an account on the Cycling Time Trials website to do this. Here's the link: https://www.cyclingtimetrials.org.uk/race-details/17526