Yes, it's possible. Me and my 3 dc live fairly comfortably on 25k+child benefit, including repayments on a relatively small mortgage.
£1800 gross, is about £1560 after tax and NI, so about £1700 net with the child benefit. Take off £300 for gas, elec and water, £150 council tax, £50 for phone/internet, £250 for food and you're down to £950 for everything else.
If you run a car cheaply then that'll be at least £100 a month, more if it's thirsty or you do more than a few miles. Still leaves you with about £800 a month for the rest (clothes, entertainment, holidays, etc).
But if you have a taste for nice things - car on lease/finance, contract phone, gym membership etc, then it'll start looking very tight. And I've not included home expenses like house insurance and maintenance as you've not said what the arrangement is for that?
Depending on your age and circumstances it might be worth putting a chunk of your savings into your pension - to get it down under 16k, if you wanted to become eligible for UC.