Insurance is a legal requirement if you have a mortgage, not optional.
House maintenance and replacing broken appliances etc periodically are also essential costs, not optional.
£9 for transport seems extremely unrealistic. That's a return local fare in many places, so you'd only leave the house once per month unless to somewhere in walking distance?
The £90 on energy and £222 Council tax is also highly unrealistic for many people - very much depends on the area and the build of the house.
Plus, if talking about retirement so living in this in perpetuity, there is nothing factored in here to pay for care, or even additional help with jobs that may become impossible to do as someone ages such as garden maintenance, DIY/ repairs, potentially also all the cleaning.
As I said, on a short term basis someone could perhaps cover their very most basic living costs with this amount (after housing) but not if they also had dependent children like the OP does, and it would be a miserable and precarious situation and not cover many essential periodic but necessary costs to maintain a home properly, so isn't a situation that it seems a good idea to place oneself in out of choice particularly if simultaneously raising children.
As you say, this only considers one single person no clothing or food for children factored in, no trips, no clubs, no activities or birthday parties or Christmas/ birthday presents and never eating out, no holiday ever. And all balancing on a knife edge where there is no reserve at all. Not ideal or something to actively choose, surely, if it could be avoided so things were more comfortable by OP working?