IMDB lists one filming location

Black Hangar Studios, Hampshire, England, UK

However, the Heaven Sent Wikipedia Entry adds

Filming for the Castle interior scenes took place in Cardiff Castle and Caerphilly Castle, in addition to constructed sets

And further links to Notes on Heaven Sent which includes the following information

We location-scouted castles: Caerphilly, Cardiff, St Donat’s (William Randolph Hearst’s house/castle in Wales, now a school), Castle Coch, Raglands, and Chepstow. Each had elements that could work, but we used only the first two — St Donat’s was a wish-list addition, but was ultimately difficult to shoot for the complicated scenes we were placing there.

IMDB lists one filming location

Black Hangar Studios, Hampshire, England, UK

However, the Heaven Sent Wikipedia Entry adds

Filming for the Castle interior scenes took place in Cardiff Castle and Caerphilly Castle, in addition to constructed sets

And further links to Rachel Talalay's¹ tumblr entry Notes on Heaven Sent which includes the following information

We location-scouted castles: Caerphilly, Cardiff, St Donat’s (William Randolph Hearst’s house/castle in Wales, now a school), Castle Coch, Raglands, and Chepstow. Each had elements that could work, but we used only the first two — St Donat’s was a wish-list addition, but was ultimately difficult to shoot for the complicated scenes we were placing there.

^{1_{The director of the episode!}}

IMDB lists one filming location

Black Hangar Studios, Hampshire, England, UK

However, the Heaven Sent Wikipedia Entry adds

Filming for the Castle interior scenes took place in Cardiff Castle and Caerphilly Castle, in addition to constructed sets

And further links to Notes on Heaven Sent.

IMDB lists one filming location

Black Hangar Studios, Hampshire, England, UK

However, the Heaven Sent Wikipedia Entry adds

Filming for the Castle interior scenes took place in Cardiff Castle and Caerphilly Castle, in addition to constructed sets

And further links to Notes on Heaven Sent which includes the following information

We location-scouted castles: Caerphilly, Cardiff, St Donat’s (William Randolph Hearst’s house/castle in Wales, now a school), Castle Coch, Raglands, and Chepstow. Each had elements that could work, but we used only the first two — St Donat’s was a wish-list addition, but was ultimately difficult to shoot for the complicated scenes we were placing there.