Note that you can only claim your VAT back once the house is considered complete, which is unfortunately open to interpretation, and it can only be applied for within three months of that date. Details of how the HMRC deems a house to be complete is available through the VCONST02530 guidance document on their website.
Building control’s completion certificate should suffice but if the house was habitable before this, e.g. with fully functioning kitchen and bathroom, functioning heating system, etc., you may run in trouble with the three month rule as the HMRC may deem that it was complete when those aspects were finished.