Rats? Hope not.
I had hu-mungus sized rats living under my dad's old allotment shed. They fed well from a local take-away outlet but preferred the country-life. Being well fed they weren't bothered with my crops so nothing suffered apart from the shed floor which provided a door into a cosy warm, extension for them. (until I dismantled the shed and dug up the oil drum - sent in the bailiffs).
My suggestions:
Look around for places where they might be nesting... and more importantly feeding.
Inform site manager / warden (if on an allotment)
Inform neighbours (if home plot) and then contact local council for advice & help
Ask around - maybe someone else has the problem and will join you in seeking a solution.
Rats can get very big - so use the holes around your potatoes as a guide to what vermin it might be. With luck it's no more than field mice or voles... little fluffy things.. not such a problem I think.
PS - Take-away closed - rats moved with the help of the foxes who moved in