You need to think a little differently about things like car repairs. They will happen sooner or later so you need to allocate some of your money every month to pay for them.
It can be useful to think of savings in two categories, firstly annual and irregular expenses that don't happen every month, but are hard to avoid, like car repairs/MOT, also Christmas, clothes for DC, a holiday if affordable and important to you, white goods replacement etc. The money you save for this isn't really 'savings' more expenses that haven't yet happened.
Savings, ie money that isn't allocated for anything in particular, but is genuinely spare money that you could use to cover loss of income should be thought of separately, so maybe try having two pots, one to pay for essentials that crop up throughout the year, that you can dip into if you need to and a separate one, that shouldn't really be touched except in dire emergency.
Of course, expectations also vary wildly and make a huge difference to your budget. Eg the average grocery spend for a family your size is probably about £80-100 pw, but there will be people who spend less, either by necesscity, or because they don't see the need to spend any more and there will also be people who spend a lot more and think £2-250 pw for groceries is reasonable, which it is if you can afford it, but equally gives lots of scope to cut back if you need to or want to free up money for other things.
Same for mobile phones. You can get a perfectly decent smartphone and allowance that averages out at around £10 pm, yet many people spend £40/50/60 pm on a high end phone and bigger allowances.