I have an Edgar Brothers model 75 air rifle which cost me £90. A telescopic sight was another £40 fitted - a nice set up for not a lot of money.
I have to say that although I bought it to shoot rats, the bloody things are far too quick - once we've seen one, by the time we've gone upstairs, loaded the rifle, opened the window, the rat is long gone.
Perhaps a better bet might be to put some rat poison down - in order to stop the hedgehogs getting it, put it in some drain pipes or tubing - rats love these tunnels and will use them - a few doses of poison and they're history.
Another option would be to get a cat !