In which building did Edward VIII make his Abdication speech in 1936?

On 11 December 1936, Edward made a BBC radio broadcast from Windsor Castle; having abdicated, he was introduced by Sir John Reith as 'His Royal Highness Prince Edward'. The official address had been polished by Winston Churchill and was moderate in tone, speaking about Edward's inability to do his job 'as I would have wished to do' without the support of 'the woman I love'. Edward's reign had lasted 327 days, the shortest of any monarch in Britain since the disputed reign of Lady Jane Grey over 380 years earlier. The day following the broadcast he left Britain for Austria.

In early December 1936, a constitutional crisis in the British Empire arose when King Edward VIII proposed to marry Wallis Simpson, an American socialite who was divorced from her first husband and was in the process of divorcing her second.

The marriage was opposed by the governments of the United Kingdom and the Dominions of the British Commonwealth. Religious, legal, political, and moral objections were raised. As the British monarch, Edward was the nominal head of the Church of England, which at this time did not allow divorced people to remarry in church if their ex-spouses were still alive.

The widespread unwillingness to accept Simpson as the King's consort and Edward's refusal to give her up led to his abdication in December 1936. He was succeeded by his brother Albert, who became George VI. Edward was given the title of Duke of Windsor, and styled Royal Highness.