You can already do 60 miles easily
The "Circuit of Cotswolds" is on the 21st of June. So you have plenty of time.
If you look at the profile
Circuit of the Cotswolds | Route details - profiles it is quite lumpy
Start increasing your mileage now and aim to have done 80 or 90 miles in one ride by early april
It's quite difficult to find the time to do this. Initially you could try taking a long route home one night a week.
If there is a cycling club near you, join them and go on their club run. These are usually 50 miles or so and quite fast. You might also want to spend a day on a sunday or saturday just riding all day.
That would be phase 1. The idea is to give you the confidence that you can do the distance
Phase 2, from early April until the event you need to work on your speed. Or your climbing. Or your climbing speed
To do this find a hill that takes at least 5 minutes to climb. Ride up as fast as possible. Recover for 10 minutes by riding around on the flat. Repeat until your speed up the hill starts to get much slower.
Another thing you could try at this stage is riding at your "race pace" but for a shorter distance. Pick a longish route and try, after approx 30 minutes of warm up, to ride at the fastest pace you can sustain for the whole period.
Don't over do it when you are training hard like this. Have rest days. If you cycle commute the day after just take it easy. Slow riding actually helps recovery.
But like Naggers says...you could probably do 100 lumpy miles next weekend if you really tried