Well, it depends what it's covering as PP said 
So the 1200 is all the non-fixed costs? Does that include: public transport, parking, childcare, gifts, any eating out incl coffees, toiletries, days out incl school trips? I know you said it includes fuel and groceries. How realistic it is depends on whether you have a big childcare bill, I would say. Otherwise it is do-able but would need active keeping an eye on. We are a smaller household, but I aim for non-fixed costs of about 700, with 200 of that petrol for work commute.
Are you counting rent/mortgage, home insurance, council tax, tv, Internet, mobile phone, elec, gas/oil, water, car insurance outside the 1200?
If you've tried budgets and they've not worked, I wonder if you are not including something in the budget? If you're paying it in the real world, it has to go in the budget no matter what it does to the numbers, otherwise things will never "work". Can you go back through a month or two of bank statements and look at everywhere the money is going, and look for patterns? Keep a notebook in your handbag and write down every single spend; that's a sobering experience but very effective for me.
I'd be worrying too if you're ending up needing to borrow at the end of every month. Something isn't being factored in. Can you start with smaller savings and work up? So on another thread someone suggested the nice supermarket meals instead of take-away, working up to cooking "fake-away" at home? Aiming to get the grocery shop in for £5 less one week, then again the next week, and keep it at that level for 2 weeks, then reduce again the following month? Jack Monroe recipes are super tasty, quick and designed to be cheap. Saus-agne is a big hit here and makes one pack of sausages go a VERY long way 
It's only when you really know your spending, that you can start to have enough control over it that you can confidently set aside an amount straight into savings as soon as you're paid. That then let's you build up a safety net for things like car repairs, Christmas, washing machines that pick the worst possible moment to give up...