If your income is quite low you may be entitled to some housing benefit to cover your rent. It is worth checking entitled.to, put in an average rent for a 2 bed property in your area, the £100 a week council tax rate and say you have 1 child under one. You should get an idea what rent you would have to pay after that.
Money saving and management tips:
Always pay the important bills first Rent, Council Tax, Fuel, Water. If you can't afford your phone bill one month it will just mean you get cut off, so long as you pay it next month it will be fine, but if you don't pay your rent, ct, water or fuel it will have bigger consequences.
Get rid of a contract mobile if you have a land line and are at home, just have a PAYG or fixed rate contract that you can't over spend on.
We save money by not having a tv licence, just the Internet and I watch recorded tv programs.
Buy supermarket own brand nappies, Tesco, Asda, Lidl and Aldi ones are good.
Buy second hand baby clothes bundles from EBay, most babies grow out of clothing so quickly that it is often very good condition. Also second hand toys, you can get massive bundles very cheaply.
Second hand cot fine, but buy a new mattress and new car seat.
You can also buy second hand prams in good condition in some baby shops and on EBay.
Buy big 5kg and up bags of rice and 3kg bags of pasta. Buy supermarket own brand food.
Walk more rather than drive or take public transport. Find a local market or get fruit and veg reduced from the supermarket at the end of the day.
Turn off non-essential electrical items and wear more clothes in winter to save on heating.
Pay the same amount of gas and electric towards your account monthly year round so that you don't end up with a massive winter fuel bill one month.
Take your food with you. Coffees, snacks, drinks all add up. If I take the kids out we take food from home. Same goes for lunches whilst at work, DH takes left over dinner or sandwiches.
Make your own baby food rather than buy jars or just give what you are having minus the salt.
Look on freegle, people often give away really nice stuff.
DH earns less than your DP and I am a SAHM (two kids, childcare too expensive), we get by ok.