Basically it's a bombproof jacket.
The linings though, they get damp and soak up filth and sweat.
First; brush it. Really, really brush it, inside and out. Use a nail brush if you don't have a good clothes brush.
Then soak it in cold water with the tiniest wee amount of fairy liquid.
That'll loosen any clamped on dirt and if you move it about lots that will help the gunge to come off.
Put it on a hanger and put it outside to dry off.
Now really look at the jacket. If it has paint on it, you're unlikely to get that off. If it has been bleached or is very faded (shoulder/forearms, backside polished if someone's used it as a farm machinery jacket) then you won't get rid of those marks. If it has frayed tears they can be repaired but they'll always look like a repair. If the lining is shredded best to just use it as a pattern and make yourself a new one.
If it still looks worth saving, then either use the laundrette as you suggested, or see if you can find an amenable dry cleaners.
Both process will really strip the wax from the cotton, but it's the best way to get a clean slate to start from again.
Re-wax as suggested. Hang it above a radiator if you don't have a hairdrier, the tumbledrier works well but you need to clean it out afterwards with thiners to remove the wax coating on the drum
Paraffin wax is the stuff that cheap candles are made from. Sometimes they add a wee bit stearic to harden them though.
Mineral oil is baby oil. You can (gently/carefully) heat both and mix if you are really, really being tight about money.
Personally I'd dump the filthy lining and see about making a woollen one.
Best of luck with it
Toddy
