Rent relief is being phased out for existing tenancies, but it has been abolished for any new tenancy commencing after 7th December 2010. So if you move you will not be able to claim it for the new property.
Budget 2011 changes the rules on rent relief for tenants of private rented housing:
The relief will be phased out over 8 years
Claimants who were not renting at 7 December 2010 and who subsequently enter into a rental agreement will not be able to claim relief
From the above it would appear to me as you were renting (elsewhere) in December 2010 you should still be able to claim the relief.
I'd check with revenue before moving