the crossman phantom i have is almost legal limit, i think its around 11 11.5 ftlb. there is a mk ii of same rifle out around 200 quid. built in silencer which on a break barrel is pretty pointless, but excellent rifle. I have killed loads of rats with mine.22
i also use a scope and shoot accuratly at 25 yards in my garden, still has the power to flip metal targets.
You may get a secondhand tx200 for that money, i have a carbine in .177 and a great pest control springer.
I have a Gamo Maxxim Elite .22 myself, purchased after one of Andys reviews ;-) Although not a springer but a gas ram break barrel I really can't fault it, nice and light to use and the 10 shot magazine I wouldn't be without now. I've found BSA Interceptors are the pellets liked by the barrel of mine and give pellet on pellet accuracy at 10 yards in my garden. Always finding the target when out in the woods at further distances. I'm sure if you shop around you could get one within your budget. Well recommended.