No, smoking is not allowed inside any of the royal residences or palaces in the United Kingdom, including Buckingham Palace, Windsor Castle, and Kensington Palace. The British royal family has been very public about their efforts to promote healthy living, including giving up smoking.

Queen Elizabeth II, who is the head of the British royal family, has never been a smoker, and she has been an advocate for healthy living for most of her reign. In fact, she banned smoking in all public areas of Buckingham Palace, including offices and staircases, in 2003.
Prince Philip, who was the husband of Queen Elizabeth II until his death in 2021, was known to be a smoker in his younger years. However, he gave up the habit many years ago and was often seen promoting healthy living and exercise.
Prince Charles, the eldest son of Queen Elizabeth II, has also been an advocate for healthy living and environmental sustainability. He has spoken out against smoking and has been involved in campaigns to promote healthier lifestyles.
The other members of the British royal family, including Prince William, Kate Middleton, Prince Harry, and Meghan Markle, have also been vocal about the importance of healthy living and have been involved in campaigns to promote healthier lifestyles.
In addition to promoting healthy living, the British royal family has also been involved in anti-smoking campaigns. For example, Prince William and Prince Harry participated in a campaign to raise awareness about the dangers of smoking, particularly for young people.
Overall, while there may have been members of the British royal family who smoked in the past, smoking is not allowed in any of the royal residences or palaces, and the current generation of royals is very vocal about promoting healthy living and a smoke-free lifestyle.