Twickenham is in West London, south of the river, and part of the Borough of Richmond. It's the home of Twickers, where England plays its international rugby matches and it is also the home of Strawberry Hill House, the home that Horace Walpole (1717-1797) the youngest son of England's first Prime Minister, Robert Walpole, built for himself in the late 1740's and continued to add to over his lifetime. I visited Strawberry Hill House when I attended the London College of Furniture--I have the brochure from when our class visited--but I don't remember going there. And yet I want to recommend it as yet another house in London worth the trip. The style of the house is Gothic and is, as such, unique being, as far as I know, the only 18th century house built in London (open to the public) in that style. (There are others around the country which I have visited such as Croft Castle in Herefordshire.) Walpole's vision was well in advance of the nineteenth century Gothic proponents such as A.W.N. Pugin (1812-152) who designed the House of Lords. Walpole was not, as Pugin was, invested in the idea that Gothic taste (not just in architecture) was the emblem of the true church of England, meaning Catholicism. Walpole's Gothic predilection in architecture mirrored his literary bent as he wrote the first Gothic novel--"The Castle of Otranto", published in 1764--but his forte was self promotion through his wit and social criticism. His house is really a statement about himself which I would interpret as being different, not part of the herd. He likely influenced William Beckford (1760-1844) who built a Gothic house, Fonthill Abbey and also wrote a Gothic novel, "Vathek". (Fonthill Abbey has only a small section still in existence as the tower at the center of the abbey fell in on itself.) English eccentrics, by no means a pejorative term, can have very long after lives.
There have been some extraordinary sales of notable collections over the years. Strawberry Hill House had a sale in 1842 that lasted 32 days and some of the finer things in the sale are now in galleries in London and elsewhere. (Interestingly, Walpole's father, Robert's collection of paintings, was sold in 1779 to Catherine the Great of Russia.) A Walpole devotee and scholar, an American, W.S. Lewis and his wife, Annie Burr Auchincloss Lewis, collected and amassed a vast archive of Walpoleiana which is located in Farmington, Ct. and is a part of Yale University. But Walpole is known to have had some great furniture items, notably a Pierre Langlois lacquer commode and, among the finest items, a pair of hanging padouk wood medal cabinets by William Hallett, one of which is in the Victoria and Albert Museum in London and the other in the Chicago Art Institute. (Unlike the cabinet in the V&A, the Chicago cabinet does not have ivory statuettes of historical figures on the pediment.) Walpole also had an interest in historical objects associated with notable people in history, a type of collecting that went beyond guns and swords to pieces of clothing or objects used by historical figures. In a word, Walpole's interests were broad and the dispersal of his goods was clearly a significant event.
That little to none of what Walpole collected is not at Strawberry Hill House should distract you from visiting the house. Gothic is a taste that is often hard to fathom but worth looking closely at if only to realize just how complex it is, particularly in revival. The vaults and the ribs of real Gothic were necessary, architecturally speaking, they aren't in faux Gothic--they are window dressing, not functional. And the Gothic style is part and parcel of the English soul--Thomas Chippendale had "Gothick" style furniture in all three editions of his "Director". Gothic follies in the landscape, often "distressed", meaning they were built as ruins to suggest the existence of a Gothic structure on the property, became fashionable and slyly hinted that the owner's family "estate" stretched back further in time than you might have supposed. Walpole was tapping into a vein that, though not often mined, was universally understood. I think you could safely say about English architecture that when all else fails, go Gothic.
https://www.burlington.org.uk/archive/exhibition-review/horace-walpole-and-strawberry-hill For an in depth look at Walpole written about the exhibition on Walpole at the V and A.