VAT on Garage Build

Our VAT registered Ltd owns a residential property which is not currently rented out. We are having a separate garage built on the grounds of the property. SR VAT (20%) is charged on this as the garage was not built at the same time as the residential property. We plan to rent out the garage as parking facilities separately from the residential property (separate tenants etc). As such I believe SR VAT (20%) would need to be charged on any rent for these parking facilities, as it completely separate from renting out the residential property which is exempt from VAT. My query (if all the above treatment is correct) would be if we able to reclaim the 20% input VAT incurred for the garage built, as technically it was built for a taxable supply. Thanks.

Hi.
The parking facilities ahould be standard rated.
Please see the guidance below:
Parking
As regards to reclaiming the VAT then please see  below which provides the criteria for reclaining VAT in relation to taxable supplies
Introduction to input tax