By chance, I learned about existence of Israeli students competition in mathematics. Its website is in Hebrew, but problem sheets are in English and are easily identifiable on the website. They look interesting;here are two samples, 2011 Stage 1 and Stage 2. Surprisingly, I have never heard about anything similar being organised in UK. There are International Mathematics Competition for University Students (organised by Professor John Jayne of UCL), but they are perhaps too remote from British students.