£1600 is the equivalent of £2400 a month gross. Being handed that per month isn't bad if you actually manage to deal with priorities first. Rent should be paid, I am assuming council tax is paid if you are on full UC, then utilities, then food.
Mobile phones are nice to have but are NOT essential. Yes, have an old TV that you got cheap, but not one that takes up most of the wall in a small room so you can't sit far enough from it and it wrecks your eyesight.
Smoking is not an essential either, so if you are broke you should stop. Yes, I know it is not that simple, but if it comes down to a choice between smoking and food it is clear what choice should be made.
My thoughts on this are that the essential bills should be paid direct through the UC system, OK I know it's complicated, but it would get them paid. Then the rest should be given in vouchers that can only be used for food. It would be illegal to use them for alcohol and tobacco.
I've seen too many people buy their cigarettes as soon as they get their money through, then a couple of weeks later they run out of food and money, but they have enough cigarettes to last the month. (Used to work in Martin's and they told me what they were doing, couple of times I refused to serve them but my boss threatened to sack me if I continued, reasoned they would go elsewhere if they had to. We weren't even the cheapest shop to do this at, they just couldn't be bothered to walk 15 minutes down the road.