As has been said you are not breaking any rules by reducing the rent but be careful mortgage payments can go up as well as down. The local housing allowance which is the maximum LA will usually pay on Housing benefit have gone down in many areas of the country recently, which often means tenants contributions increase, but represents the general reduction in rent charged.
If your tenant is paying rent under an assured tenancy I suggest you do not reduce the rent before the fixed period, usually six months, has expired then write to the tenant and provide him/her with the new rent and the date of commencement.