Councils will usually poison rats for free, especially if they are near houses. Ask them.
If it is not free then your allotment site should consider paying for it.
Rats are vile, dirty, disease ridden creatures. Do you want to eat or even handle vegetables they have peed on?
I cannot let this stand here without a comment as rats are definitely not dirty or vile. As any wild animal they clean them self frequently and healthy rats have clean and shiny fur as it is important to keep it as clean as possible to prevent getting ill.
Rats are opportunistic wild animals which try to live their live as best as possible and take advantage of our wastefulness with resources (food is even lying around on the streets). But it is a problem we have created entirely our self as we give them the chance to proliferate abundantly and live in large numbers so close to us.
I think a start would be to not give them access to food to keep their numbers down as (as others have written before me) poisoning just makes space for new rats to move in. And I also think we have to live with rats as there will always enough survive to start a new population.
And I have to admit that I find the much loved hedgehogs more dirty than rats, I just remember the last one I have seen with lots of ticks and fleas crawling all over the skin.