You may struggle to find a scope that will be properly up to the job for that sort of money.
Are you able to support the gun in a stable way and also use a scope sidewheel at the same time?
I would guess that side PX rather than something with front AO would be easier?
You might find a Hawke Sidewinder 8-82 or a Viper 8-32 for your budget, but can't say I have used either.
For a big Nikko you are realistically going to be looking at £300+
There is a new BSA side focus Quarry King 8-32 for about £130 but no idea what they are like. SOme people have found that they have dropped lucky and found a ZOS scope from fleabay etc that works for them.
Your are going to need mag above x32, and most scopes like that will have a fairly large objective lense at 50mm+
I am sure that there will be shooters on here who have good experience of budget FT scopes who will hopefully pipe up.