My puppy is coming up to a year old (already!) and I can’t remember what the general advice is for exercise at this point. If we walk for an hour on lead we easily cover 3 miles as he walks really fast and luckily so do I; he would do more but I stop him. Off lead on the park he gets anything from 30-60 mins depending on the weather (heat) and if he’s been playing with other dogs etc. He also likes running through the woods so he gets a variety of terrain to tire himself out on.

Can I just start slowly increasing what we do or do I need to keep with the 5 mins month ‘rule’ for a while longer? He’s lean and would go further but I don’t want to do too much too soon. He won’t be a weekend warrior either although in time longer walks will be at weekends.

If you're wanting to do very long hikes then I would keep increasing steadily to about 18 months old, that will over growth plate closure if he's a larger breed (my apologies, I can't recall what he is!).  Smaller breeds you could increase quicker I think as their plates will close earlier.

He’s an insane boxer hence me having to stop walks as he would just keep going until he dropped.

Are you just wanting to spend more time walking him or are you aiming to tire him?
Bear in mind that as you exercise him, he will get fitter and not tire as quickly. If you are aiming to tire him, try brain games, heel work, impulse control etc.

Over time more building the distance. We do mental stuff anyway so it’s building stamina for longer walks and maybe even jogging rather than just to get him tired. He’s fairly chilled out in the house which I like so no I’m not aiming to run him until he drops to tire him out; sorry if I didn’t make that clear. I certainly do not want to create some sort of exercise monster that’s just go go go all the time.

Due to his breed size and propensity to heart issues (and the short muzzle effect on exercise tolerance) in the breed, I would keep adding the 5 minutes/1/4 mile per month of life to two years.