A winter coat is not a luxury - it's a necessity. As are shoes, school uniform, heating, etc.
Luxuries are Silver Cross prams, top of the range mobile phones (although every adult needs a mobile of some sort), booze, fags, nights out, trips to the cinema, holidays, etc, and I would argue that if benefits provide that level of support to people then they're too high. Benefits should pay for the basics, that's all.
However, I am very much opposed to the cutting of services like Sure Start centres, libraries, parks, etc. Sorting out benefits so they aren't a lifestyle choice and ensuring that work pays are widely supported and broadly good ideas, but our services in this first world nation should be the best. Good education for all, access to libraries and play equipment, parks that are free of litter and dog shit, world class mental health care, excellent healthcare, and enough council houses so that families aren't living in B&Bs or crammed into single rooms. People can't better themselves if they don't have access to those things.