You will have to cut back unfortunately. You can't have your cake and eat it too. Being single is expensive you have to play the long game, life gets better but it's tricky to begin with.
When Dd was small I had a PAYG dumb phone, no Internet, no car. I was fortunate to be eligible for a council flat but I still had to go without those things even though the rent was low.
As DD got older and went to nursery I got a 16 hour a week termtime only admin job. When she went to school I changed roles internally to a 20 hr role and earnt more. I could then afford broadband and a smart phone.
I then changed employer to a different school as a TA more hours again term time only, studied a degree in the evening and bought a car. When I finished my degree DD had started high school, worked as an unqualified teacher during the end of my degree, decided teaching wasn't for me so I moved to a different employer which was a normal hours all year flexi admin role 3 days WFH, DD didn't mind being at home during the holidays and work up half way through my work day anyway and would be out with friends during the day or wed go out to the beach etc in the evening.
Each move I made had to be gradual, term time only roles during school hours as I couldn't afford childcare or used after hours childcare with 70% paid for by govt. You have to play the long game, all the moves had to work towards me being financially independent for when Dd finished education ie I couldn't stay in the TA role I loved as I couldn't afford to. Then they bought UC in I had to work towards that goal faster as I was on the old tax credit system and wouldn't be eligible under UC.
As far as DD knows she had a great childhood, we live by the beach so went often, we did lots of fun free things in the community, regular library visits for activities and to borrow books. We went on holiday but they were city breaks in the UK in a Premier Inn, London when Kids week was on so kids go free to theatre shows, Butlins during term time, Disney land in February etc. For birthdays I'd ask family for annual passes to various local attractions, our local paper does a token scheme for the nearby Sealife centre so you get access for a year for £10 and a couple of tokens. Instead of making lunch to eat at home make up a flask and pack lunch (or dinner) up and eat at the park, beach or woodlands. One winter we decided to visit every swimming pool in the cou ty during their fun session to see which one had the best one. These things all make for a cheap but great childhood.