How far do I need to be able to run realistically

No one expects you to be superman, running 5k regularly is a great baseline for when you start basic training

Park Run is a great way to get started.

Not at all, if you can comfortably run a 5KM at the min then you are at a great place training wise to start basic training...
I would even say you can focus less on the running and start focusing more on doing static exercises such as press ups and sit ups....
This will ensure you have a good all round level of fitness.

What you’re doing is great and will make a great base fitness to which can be built on in basic training for more army specific fitness

The Army have a great fitness app too for you to follow.

Thank you both, I'm having a bit of trouble doing pushup as I am a bit of a heaver guy so I was wondering if you had any tips on doing them. Thanks

You will be required to run 2K at assessment centre in 13 minutes 10 seconds.

Get yourself on YouTube there are plenty of army videos made by PTIs

Thank you

Try and get into a routine of doing a set amount each day, practice makes perfect!

I run 2.1 miles a day do I need to run more

I think you can vary the distances and pace that helps