It looks like your budget is approximately equal to income, so in practice you'd be able to squeeze in with minor adjustments. (For me, Sky is one of the best-value-for-money items on the whole list, and the last discretionary item I would cut. Internet is more important, so important that I wouldn't even consider it discretionary.)
I've recently discovered that washing M&S washable suit trousers on hand-wash cycle with wool detergent really does work. (And it definitely works a lot better than actual hand-washing which leaves them a lot wetter and more prone to creasing.) Have only done this once, and hung trousers over banister to finish drying, and when dry they were ready to wear, with original creases/pleats intact and no new creases added, no ironing required. I take the view that suit jackets don't need cleaning at all. That was my view even before I gave up buying/wearing them, after I realised I only ever wore them to walk 100m between office car park and car.
I don't need a mobile, as I'm always either at home or office where I have a landline, or driving between the two, when I can't use one.
My contents insurance (£25K contents in a flat in London) is £100 a year.
My electricity and gas is £100 a month. (Well-insulated modern flat though, so your estimate may well be nearer the mark.)
Your grocery budget seems high, our spend for 3 is roughly £100 a week and I think we could spend much less if we had to. That bill includes child clothes which often come from supermarket.
My car insurance is only about £300, but I think that is lower than average, so your figures may well be more accurate. Also, although I only drive cheapish (£4000 - £7000) second-hand cars, this still costs me approaching £200 a month in depreciation and maintenance, on average, so you need to budget for that. (I do use main dealers for servicing, and replaced a gearbox for £1500 once, so without that it's possible your figures could work out a little lower.)