"Just for reference, I am a single parent and have nothing whatsoever to leave my children, which is why I didn't think I needed a will. I rent where we live and have no savings. Please could anyone advise do I need a will?"
In your situation, the main thing about having a will is to provide certainty for your children if anything were to happen to you before they get to the age of 18.
Would you want them to go and live with your ex for example? If not, then your will should include naming a guardian to care for your children and a trustee to look after their money (this can be the same person).
.
"What do you even put in one? and are they expensive"
It can literally be something as simple as "I leave everything equally to my children and I appoint XXX as their guardian"
As to cost, a number of charities offer free will writing services (they often ask that you leave something in the will to them in return).
Here is a whole list of charities that do this:
https://www.nationalfreewills.net/charity-logos/
.
"how can the LA decide it is a deprivation of assets, if it genuinely wasn't and at the time of gifting my father was in perfectly good health? What do they do?"
Deprivation of assets is where you deliberately give away your assets for the main reason of avoiding care home fees.
Intention is the most important factor to consider. When you gave away the large sum of money or transferred your property to a grandchild, was it reasonable for you to expect to need care and support?
The local authority must prove that you were aware that you might need care in the near future, otherwise, there is no deprivation of assets.
Frankly, selling a rental property is not going to be a problem (unless he's recently been told that he needs to go into care in the very near future).
.
"Can I also ask if the money goes into each child's saving account, if I were to die, is it in their name, so they can just access it? Meaning, that their remaining parent (my ex) would then have full control over using it (probably for himself) if they were still under 18yrs? What rights or control could they have?"
The accounts will be in each child's name and show you as the trustee. If you were to die before they were 18 then they would not be able to access the money, another trustee would need to be appointed.
If you named somebody in your will to be that trustee then they would look after the money. If you did not name anybody in your will then (if he has parental responsibility) it would be your ex that would have control over the accounts.
.
"Who can access premium bonds? Only named adults? or children? I don't even know how you get them! Are they worth having?"
I would disagree with the posters who mentioned premium bonds. No, I don't think they are worth having.
I would suggest opening a children's savings account for each child with you as the trustee. Pay the money into each of those accounts.
https://www.moneysavingexpert.com/savings/child-savings-tax-free/
Then think about putting some of the money into a Junior ISA. You can put in up to £9,000 into a Junior ISA, so you won't be able to do it all at once.
https://www.moneysavingexpert.com/savings/junior-isa/
Any money that you put into a Junior ISA you cannot get out again until they are 18. So it might be worthwhile keeping some of their money in the savings account in case something comes up before they're 18 that they might want to spend some of the money on.