So my bike came with Formula rotors, adapters and centrelock wheels.

Theres play in the centre locks which has definitely got worse over the life of the bike, to the point i can now move the bike about 3 inches with the brakes locked.

If I buy Shimano centrelock rotors will these work with the formula discs?

or should i just by new adapters and hope for the best

Can you work out where the play is? If it’s between the adapter and the rotor, then a Centrelock rotor will resolve the problem.

If it’s between the hub and the adapter then a Centrelock rotor may resolve the problem (it will depend on whether or not the splines on the hub have worn).

You should be able to use the Shimano rotors with the Formula calipers but you might have to re-align them slightly.

If the lock nuts are not tight enough you get play. Play leads to more play.

You could try wrapping a little bit of PTFE tape around the splines and then doing up the lock nuts really tight. The tape will probably bunch so don’t put too much on or it will mess with the disc alignment but should help pack it out enough provided you do up the locknuts tight.