For one person, maybe. For a couple, probably not.
When I need to be I can be really frugal, but 10k a year is only £833 a month. My bloody council tax in an average area is £210 a month.
Although your OP says not to cover housing costs I've assumed this means mortgage/rent. Or did you mean council tax as well?
Water, gas, electric, home insurance are another £200 in total per month for us at the minute. Including council tax above that would leave £423 for everything else. Food, (has anyone noticed how much food has gone up by recently?!) petrol, car tax, insurance, saving a bit for repairs, tv licence, broadband would eat up most of not all of that quite easily.
..and that's before even thinking of other "luxuries" like saving for Christmas and birthday presents, days out, meals out, holidays, haircuts, dentist appointments, clothes etc.