Op if you're still here after the shit tonne of unnecessary unpleasantness:
Avoid BHF shops, total ripoff who I've seen sell cheap mfi type things for more than original price new.
See if there is an Emmaus near you, charity that homes formerly street homeless people and trains them to renovate and restore furniture / white goods which are sold to find the Emmaus community they live in, great bargains and will deliver too.
Sense charity shops and Sue Ryder also do decent second hand goods at good prices.
Local credit union is a great place to go ask about loans, even if on low income, got my fridge that way; helps build up savings even if only in pence at a time to cover future expenses.
Ask at local library for the books that list charities / grant bodies and what they cover, can get grants for all sorts of things for all sorts of niche groups, if one of your parents worked as a hat maker you could get a grant for stuff for example, worth a look.
Utility companies offer grants for various things depending on family circumstances, not always well advertised so worth looking around web / their websites to find out.
Local area Facebook pages - fab for finding free furniture / white goods, loads offered in our area and it's not that well off an area; and gumtree also a great source.
Check with the HA whether decorating vouchers are available, I'm with L&Q and they give vouchers for b&q, amount dependent on number of rooms.
Best of luck with it all, it all feels overwhelming when it's so sudden, but will work out well in the end when you've a safe secure home for your family 