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Roy Wood didn't actually play that solo, as far as I'm aware. I think he just pretended to, although I'll stand corrected.
Nothing suggested so far is really suitable. It's all a bit cheesy and cliched. Not quite Baker Street but getting there. Also, when you've just got a piano to accompany you, you don't always get the full effect, and that's exacerbated much of the time if what you're playing is a song tune. A lot of songs just don't work without the words. You either get a very short or a very boring performance.
Classical (or classical style) is fine, as is light jazz, although it can't be too complicated because as I've said, I don't have much time to work on it. Folk's OK too - my favourite singing genre, actually.
I've found a couple of jazz numbers that might be worth singing, as well as a music hall song, and I'm about to have a browse through a book of Benjamin Britten folk song arrangements for something not too difficult.