My white t-shirts are going grey - how to keep them white?

Fed up with having grey tee shirts, I bought new white ones and only washed them with themselves or with newer white tee shirts.

Trouble is I do do gardening and construction work, so they probably do get sweaty and dusty.

I have a cheap old Bush washing machine I was given and don't intend to replace until it breaks but it seems to work and wash quite well, as far as I can tell. I wouldn't say it's worse in wash perfomance than the old Miele that I managed to lose (long story).

I have used Dr Beckmann Glowhite in the past, but it seems too expensive to use in every wash and did not seem to do anything obvious.

Given the environmental issues associated with cotton production, I'd rather not ditch some perfectly sound tees just because of their colour.

I use "Ecoleaf" liquid non-biological detergent because I can't stand the smell of perfumed detergents: they make it hard for me to breathe and my eyes water. I do not use softener for the same reason. I also do not wear perfume, anti-perspirant, or similar product.

I air dry my washing, preferably outdoors.

AND the tee shirts still slowly go a light dull yellowy grey. Chlorine bleach doesn't seem to touch it. I will try oxy bleach, and I need as many tips and tricks as people want to give. So anything is appreciated. No point asking my parents - laundry really is not their strong point.