Agree with seren. First thing to do is, as you identified yourself, work on your endurance. Get more slow miles into your legs... so you're doing a good long run once a week (working steadily up to at least an hour).... and 2 (or even 3 or more?!) shorter ones in the week... maybe half the distance of your long run.
Ideally, stop doing your park run every week... or it will stop you having the weekend to available for bulding up the slow miles - which are vital. I suggest being patient and build up the slow miles for 6 weeks before next having a tilt at the park run. But if that takes away your enjoyment/motivation, then carry on enjoying your park runs,,, enjoyment is the most important thing!
In just 6 weeks, you might even take another 4 minutes off your PB if you follow that plan. Then it might be the time to introduce a speed session, perhaps one week doing a few intervals.... and the next week doing throwing in a 'fast' mile into one of your midweek runs. That's the time to start re-evaluating where you're up to.
Good luck!