Within Kew Gardens, is Kew Palace, an actual royal palace, most closely associated with King George III (it’s where he was kept when he was having his spells of madness, but was also the family summer home).
It’s a surprisingly small place (and that’s even knowing there was another wing there when the king was in residence). Inside, there are exhibits about the king, and about daily life in the palace.
Next to the palace are the Royal Kitchens, which have a charming kitchen garden, and some pretty extensive rooms you can wander around in. Definitely an interesting peek into life during the 18th century.