Congratulations!
You will be fine.
The basic bills are
Gas
Electric
Water
Council tax
TV licence
Telephone
Internet
Set aside roughly £300 for this and make it direct debit, it is cheaper. BT gives you the option to pay line rental in one go, about £120 for the year, makes it much cheaper.
Insurance, MOT, service for the car and petrol are another expense you need to budget for. With my car I need about £500 a year, roughly, petrol on top, I spend about £150-200 a month on petrol. Add all your sums together then divide by 12 and see how much you need to set aside for this.
Food wise, we are 3 and I spend about £40 a week in Lidl and one shop in Sainsbury's for stuff I can't find in Lidl, about £60. I cook from scratch. The treats are mainly baked on a saturday afternoon, biscuits, cake etc. i found it helpful to menu plan and set days for certain ingredients, eg: tuesday egg night( eg:omelette), friday pasta, monday rice etc. gives you a rough idea what to cook.
To give you an idea, twice a year I need about £150 for kid's clothes and shoes. I am not adverse to second hand so I buy a mix of sales and charity shops. Mine is a bit older, so she needs school shoes, boots, crocs, flipflops and trainers, once or twice a year, I never buy second hand shoes. I have a girl and often buy dresses that in a couple of years'time turn into t-shirts/tunics worn with leggings. Sometimes you'll find in sales things your child would be able to wear next year, buy it and write it in your diary for the appropriate month: she has winter jacket ! under October,for example, for a coat you bought last march, because of sales. Or: school shoes, under august, maybe july as well, so the expense doesn't catch you unexpectedly, gives you time to budget.
You'll be fine:)