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If you think you're going to wear it more than once I'd probably buy one rather than rent. I got one from M&S I think that wasn't much more than the hire fee and didn't seem much different to the hire suits.
If you've got the time then I'd definitely go second hand, there are plenty out there and they go for very low prices in the main.
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There's tons of nice tuxedo stuff on eBay.
If you know which size you are and have normal length arms and legs, something nice/not serious but appropriate should be doable for little money.
If you're as skinny as I was 20 years ago there still is a nice but scruffy 40s Harrods dinner jacket in my wardrobe if I haven't sold it at fleamarket? (That tells you I am definitely into clothes.)
Then get those and have a new pair of vegan docs that will outshine all other shoes?
https://eu.nps-solovair.com/collections/mens/products/vs3-995-bk-sm-veg-g
Where's good for black tie rental in London? I'm off to a frustratingly boujie wedding at the end of summer.