DD has cup with integrated straw. It does come apart into three sections - but the inside is just beginning to look a bit manky nonetheless. Running really hot water through or leaving to soak doesn't seem to be enough, as there is a kind of valve I think it in to make it more awkward.
Mine is a mothercare one - it kind of has a flippy bit which covers the bendy straw which then pops up. The straw does split into two - and one bit you can run hot water through, the other bit you can't really because of the valve which seems all integral to the straw. Anyway - thanks for the advice - I think cotton buds and a baby bottle cleaner are all too big to fit in the straw itself, but I'm trying to track down some pipe cleaners, and will also try sterilising fluid!