We have 3 and household income is about £35k. Our youngest starts school in September and I'm job hunting. I've done some part time work since she's been born but my husband is currently the only earners for various reasons. Prior to her being born I was working part time and before our second was born I was full time.
I think doing it on a low income is doable if your outgoings aren't too much. Our mortgage is £750 and we always fix it for 5 years to try and ride out any uncertainty. I am very frugal and spend a lot of time managing our finances very carefully, shopping for deals and planning carefully. I save for everything across the year - Christmas, birthdays, holiday, car service, mot etc. We put money away every month for children's clothes, haircuts, prescriptions - basically, everything you can think of. It means we have a fairly large pot to pull from when things happen. What this means is that we don't really have much left for fun stuff. Most of our fun stuff involves free community events, woodland walks, picnics in the summer, beach trips (mostly to beaches with nothing that needs paying for) etc. When freebies come up we do those. Because we save money each month in the way that we do, it means that quite often we over save (eg car service and insurance usually come in cheaper) and so we can use that for things that we want to do like take the kids to the cinema or a meal out. We manage to do one paid thing a month.
We have an OK amount in savings and no debt. We manage well, but we have no prospects at buying a bigger house at the moment, or a new car which we'll need soon. We need new carpets and furniture, but we manage and cobble together.
Finding a job is important to me but it will only be part time for now as our children have lots of hospital appointments and additional needs so we need to find a balance. The plan is several years of me working part time to give us the ability to save more so we can move house and get a new car and then I'll go full time and we'll move.
I think a strategy is important if you're going to have a larger family, not on a high income.