Looking at your outgoings, I'd bin Sky and get Plusnet, which will save you £25. Look at your insurances - our combined buildings and contents is £180 pa, half of what yours is.
You're stuck with the credit and car payments for now, but get those cleared as soon as you can (we never spend more than £1,000 on our cars, and bin them if they need an expensive repair. Every now and then, we get a duffer, but I had 3 years of trouble free motoring from a £600 car). And could you manage with just one car?
Once you've paid for the phones, don't get an upgrade but go for a SIM only deal, or stick with what you've got and renegotiate the contract. (Mine now costs me £7.50 a month).
Our income is virtually the same as yours but we don't have childcare costs. All our bills and shopping, after the mortgage, are well under £1,000 a month and we run 2 cars, 2 motorbikes and a motorhome. We eat out quite a bit, drink wine and go away a lot. Despite buying clothes and treats, we're both saving regularly from our individual spending money. But we don't have Sky, credit repayments or expensive phones.
Definitely look into whether you'd be better off on reduced hours. If it means you get some tax credits and don't have to make student loan repayments, you could be quids in.
As a babyboomer, I had to chuckle at "eyewatering" interest of 4.5%. I can remember how much better off I was when I managed to remortgage at a bargain 13.1%. Most of my friends were paying 15% or more!