Hi @Interestedandcurious , I am no longer in the UK, but pretty much everyone predominantly used NHS services. There are no private Jewish Medical Insurance companies that I know of, (or if there are, that cater only to the Jewish community). Some people do have private medical insurance, but percentage wise (based on nothing but opinion!) I would hazard a guess that is probably somewhat inline with UK population norms.
Perhaps you are thinking of hatzala, the Jewish volunteer ambulance service? It's not private, it is community fund raised, and staffed by trained volunteers from the community. There are hatzala branches worldwide. I live in Israel, and both my parents are actually hatzala volunteers.
There are definitely additional costs being part of the community; Kosher food is more expensive, for example. For tuition, there are systems where you can pay according to your means. There is also a huge amount of charity giving (we are meant to give away min 10% of our income to charity as standard), and funds/free loan societies for everything you can think of, so a lot of costs are shared. For example, there is a medical equipment gemach (free loan society), years and years ago my little brother broke his leg and couldn't walk, we were able to borrow a wheelchair, things to cover his leg in the shower, and other equipment. Another example is when making a simcha (celebration), lots of friends and family will contribute help, or food, and you can borrow tablecloths, centrepieces, chairs, tables, fridges/freezers, for a nominal cost (either a deposit, or a small donation to keep things going). These are often set up in someone's memory after they pass away, as a way of continuing to do good deeds in their name. There are also numerous charitable organisations for everything you can think of; mental health support (and phone line) (e.g. JAMH, Neshomo), a lot for children with disabilities or neurodiversities (e.g. camp kef, special spirits, the friendship circle), supporting single mothers (emacare), food and groceries for families living with poverty (toimchei shabbos - they do weekly food parcels), financial assistance before the big holidays (I think toimchei shabbos as well, but there are other groups too), medical assistance/equipment/rides to hospital (ezra care). That's what I can think off the top of my head.
Gemach's can be big, or just a little thing people do from their house, e.g. a breast pump gemach might start with only a few sets, but people will hear about it and donate there set when they are finished with it, and then people only have to pay to replace the consumables.
So on one hand, costs are higher. On the other hand, community life means some of the bigger costs are shared, and their is a safety net in a lot of areas.
I can't personally tell you about how large families live on benefits; in the UK DH and I both worked. Clothes; my kids mainly wore supermarket/primark/next sale (I miss next sale!), and hand me downs. Food was a lot! I did do some cost saving things where I could (when I was working less), e.g. at one point I would buy whole chickens and cut it up; the carcasses and wings made chicken soup for friday night, the legs were also friday night's meal, the breasts were shnitzelled - another meal, and then the chicken from the wings and carcasses I froze and when I had enough I made into a pot pie, and then leftovers on Monday night. Now I still cut up the chickens, but that is preference, but I don't bother picking out bits for pot pie; not enough time. We rented for years, had a small 3 bed with 4 kids.