There was a documentary about prisoners who used bags full of water to get strong whilst in their cells (don't know what the bags were made of or how they got them).
Really, anything heavy with a good grip works. However, dumbells will make you feel more serious.
If you get a belt (not a lifting belt, a belt that you can thread weights through), a pullup bar, a couple of plates and a weighted vest, you can add resistance to a ton of bodyweight exercises.
1. Use your body weight .... but eventually will get bored :P ---
2. Do what i do ... I tied up all the "not needed" uni prospectuses i had and used them as a dumbell :P ... anything would work really --- a school bag with something heavy in it i.e books etc
A gym membership costs £10-20/mo. This should be affordable to most people if they care enough. Buying home equipment generally works out cheaper over time but it's a bigger up front cost. Take your choice.
Saw a prisoner once using his wrapped up matress to perform an overhead press
You can perform pull ups at your nearest scaffholding site
Pop into sports direct and use their weigths in store but they're not much
Push ups require no equipment but you can wear a rucksack with books in to add weight
Tricep dips between benches also need no specific equipment and you can easily add weight via books etc
I remember housemates on big brother would often use household objects like chairs instead of dumbells
Loool I can just imagine OP hanging around a scaffolding site to do pull ups while workmen are hard at work around him, or covered in sweat mid workout in the middle of a Sports Direct