Sainsburys have recently introduced their own-brand disposable training pants. They're like a pull-up nappy but more generously cut so little people can really take them up and down themselves when they need to go. My son wears them overnight (he's dry in the day but not ready for nights yet) and we've never had a wet bed. A pack of 15 costs £3.99 which is much less than Huggies pull-ups. Strongly recommended!