Bless you - that's tough.
It kind of depends what he is interested in - if he likes films, maybe you could watch one together - or a match on TV if he likes sport, and the matches are screened? If you can run to some popcorn and coke we well, or some chicken nuggets and fries (home cooked) or whatever he likes, this would make it a bit more of an event.
Local teams are often very cheap to go and see - could you go along to a lower league football match together for example?
If he likes skateboarding you could offer to go and watch him?
Cooking together?
If he is artistic, let him paint a mural in his room? (If you can afford the paints).
This one needs a bit more planning, but if you have a tent and sleeping bags, wild camping/very cheap campsite? Buy a disposable BBQ - few quid from Poundland or similar - and cook cheap sausages and burgers. Maybe roast marshmallows too.
The above could even be done in the garden if you have one.
Even board games - I "make" my daughter play Scrabble or Top Trumps or something like that with me occasionally, when I feel we need a bit of bonding time + she pulls a face about it at first, but deep down likes the fact I want to spend some time fully focused on her, I think..... She's pretty biddable tho - I know not all teens would go for this.
He may of course not be keen to do these things - I wouldn't push it - but show the interest, make the offer....Just make it clear you are interested in understanding more about the things he likes, and happy to spend time with him when he feels ready.