I've recently had a similar problem:
I have an enclosed garden which is used by Cardiff Hedgehog Rescue
for 'soft-release' for rehabilitated Hedgehogs, prior to their return to the wild. At the time, the garden was also home to a non-releasable Hedgehog, who had to be fed each evening.
My neighbours encouraged rats on to their property, by leaving a large pile of scrap wood/metal, which a family of rats took up residence under. The rats soon began to kill most of the frogs in my garden, eat food put out for the birds, and also to eat the Hedgehogs food.
Rats can attack Hedgehogs, particularly the young and sick, and they will eat all
their food. Therefore, I had to try to remove the rats or at least deter them. Firstly, I brought in all my birdfeeders, and ensured there was no waste food hanging around. Also, I would wait for the Hedgehog to appear, before putting out his food, and would stay in the garden until he had finished it.
I also purchased 3 live-catch rat traps, of a kind that posed no threat to Hedgehogs (traps will only work if there is no other food source). Eventually my neighbours, having had a 'reality check', removed the scrap, and called the council in to put poison down. Poison wasn't an option in my garden, but it did solve the rat problem.
So, basically, if you put out food for the Hedgehogs, the rats will almost certainly eat it. If you're not able to 'stand guard' whilst the Hedgehogs eat, then your only real option is to stop feeding them until the rat problem is dealt with. I certainly wouldn't suggest poison, as it is just as likely to kill the Hedgehogs, but perhaps live-catch traps should be considered.
I hope you find a solution, as Hedgehogs are in such dire straits at the moment, that they need all the help they can get.