I think I’m getting quicker but any advice on nudging the distance up?
Take it easy, and it’ll get there. Add at most 10% extra time/distance per week. When you can comfortably do 6-7 miles you should start thinking about different types of run, things like doing a shorter interval/fartlek run midweek, long run at the weekend, that kind of thing. But I personally wouldn’t worry about that at the moment when you’re still “struggling to go more than 4 miles”.
You haven’t said how many times you go running per week, but assuming you’re doing 2 or 3 outings there’s no reason you couldn’t make one of them a parkrun.
And if you can/need to, lose weight 🙂