I totally agree with @Geamhradh
I'm a perfume blogger and I firmly believe that cheap perfume can smell good. I've been blogging for nearly ten years and I have loads of suggestions. I don't believe you have to spend a lot to smell expensive.
All perfumes are made by professional noses/perfumers, regardless of the price. Even Avon uses some very highly regarded master perfumers such as Olivier Cresp and Alberto Morillas.
So here's my pick of perfumes under £20 ( and thanks for giving me the idea for my next blog post)
Calvin Klein Contradiction - a frosty woody rose that's under £20.
Paul Smith Rose- a classic and under £20
Coty L'Aimant - really smells like Chanel No 5 but is about £6 and has been around since 1927
SJP Lovely and Stash- I find it very long lasting and to the PP upthread who said she could have picked a better perfumer than Coty- Coty are behind a lot more than you might think and is a highly respected mega brand.
Rihanna Reb'l Fleur- reminds me of La Vie est Belle and lasts HOURS.
Lanvin Arpege - a huge aldehyde floral classic for under £25 for 100ml EDP.
Obsession - a timeless spicy amber that's still great and still cheap.
Next Just Pink - reminds me of Ralph Lauren Romance
There's lots of great Avon ones too. Try Tomorrow- reminds me of Givenchy Organza and was made by Olivier Cresp (Angel, Black Opium etc)