I have a remington 700 chambered in 7RUM and i was givin a muzzle break that fits. However the muzzle break is for .338RUM since the diameter is bigger will this work and would it effect accuracy?
It will work fine.
It may lose a little efficiency as there is more clearance for the bullet than needed, but we are talking about very small losses.
Perhaps 5% or maybe 10%.
You would not be able to feel the difference between that brake installed on your rifle and one with a slightly smaller exit hole.
The benefits of a tight fit between the bullet and muzzle brake exit hole are greatly exaggerated. I like to bore them about .030 over bullet diameter. But a hole as much as .080 over doesn't seem to reduce the effectiveness.