I'm 20+ years older than you, can do 24 min 5k and run 3 times a week totalling around 12 miles so there's no reason at your age why you can't beat me!(assuming you don't have any disability and aren't massively overweight)
If you run 10m or 20 or 30 a week at your 5k pace you won't get any faster, you need to do some shorter sessions at faster speed, replace one 4 mile run each week with either
5 times 1k with a minute rest in between at your target 5k pace
200/400/800 metres repeats with rest in between.
hill reps - run fairly hard for 50?, 80? 100?m up hill, jog back down and repeat
If you always run at 28min 5k pace you'll always run at that pace, you need to learn to run faster and if you have limited time available it's quality that matters not quantity.
Think if it like learning to read. If you had always read the books you had when you were 5, when you picked up a more difficult book you wouldn't able to read it - it wouldn't matter how many times you read the easy books you'd never be able to read more difficult ones, you have to read slightly more difficult ones and whereas you could read the whole of a 5yrs book easily, you'd have been knackered at the end of a page of a more difficult one so gradually read a bit more.
Running's the same, if you keep doing the same thing you keep getting the same result.
parkruns exist in places where someone who lives there decides that they want one, not because HQ go looking for somewhere to start them so it's down to the locals to get it going.
The reason they started in Poland was that a Pole was living and parkrunning in Newcastle and when he went home he took the idea with him and 2 of the US ones were started by people going there from the UK. If someone contacts HQ and wants to get them going in their country then can do.
There are moves to get started in France - I know the volunteer roles were being translated into French recently. I think I've heard that there's a change happening about the medical certificate, can't remember details.
When you say that they aren't as widespread as you'd have thought, they've gone from 1 event with 13 runners 10 years ago to about 550 events and over 90,000 runners per week in 10 countries from NZ to US so that's quite widespread for an event with only a handful of staff working from a garden shed in West London!
"Getting back to hotel near start. The roads will be open from 11.30 to get a taxi (there’s a rank on East Street, probably taxis around in the Old Steine) or the bus 5 or 5A from outside the pavilion (on the Steine) BUT the traffic is generally horrific, even though there are bus/taxi lanes it might be quicker to walk, depends what’s more important, the time to get there or the ability to walk another mile or so!
Getting from Seafront to start. The direct roads are closed from 7am so no buses or taxis that route. It's not worth getting the train from Brighton to Preston Park station, that's as far as walking direct. There are always lots of people walking that way, this is probably the best choice. I don’t know how well the taxis understand the road closures, if your hotel is east of the pier tell them to go via Freshfield Road, Bear Road, Fiveways, Preston Drove and drop you by the park/bottom of Surrenden Road but you have to drive so far out of the way it’s hardly worth it unless your hotel is a long way east. If your hotel is West of the pier they can go to Seven Dials then either drop you at the bottom of Dyke Road Drive or go down Millers Road and drop you at the bottom of the Drove / South Road near the shell garage but it’s still marginal if it’s worth it unless your hotel is a long way west of the pier. Have a look on Google maps to make sense of this."