I would like to "nanny" at the weekends as a part time job
I find that there is not much demand for weekend childcare. You may get the occasional Saturday evening but I find that daytime care is quite rare. Have a search of your local area for adverts from parents looking for weekend childcare... you may find a few on ChildcareCoUk, Gumtree, local Facebook Group, that sort of place.
You have qualifications, DBS check and you have nursery experience. Your best target market is probably parents of children who you already care for... does your nursery let you offer childcare services to parents of children attending the nursery (check your contact, ask management).
Do i have to sign up to OFSTED if i was looking after the children at their home?
No. Childcare in the child's own home comes under an exemption from registration. Some parents may want to use Tax-Free Childcare or childcare vouchers, so to be able to accept those you would need to be Ofsted registered on the voluntary part of the Childcare Register. Initially I would not bother, as it costs and takes quite a long time... so I would focus initially on find out if there is any demand and getting your first couple of clients.
Do I have to set it up through the government so they can take taxes and stuff, I haven't earned anything yet.
No, initially you can use Trading Allowance. This enables you to earn up to £1000 without needing to register your business.
Keep in mind that ad-hoc childcare could be done via your business as a sole trader but permanent childcare is employment. So if a family wanted you to work every Saturday then that would be employment and the parents would be your employer and responsible for reporting to HMRC.
Can I just accept cash & BACs without the parent signing up as an "employer" ?
Yes, though do simplified accounts. It is called Cash Basis accounting with Simplified Expenses. Record each transaction when it happens, so when a parent actually pays you, not when you actually do the work.
Small Business Accounting by Andy Lymer is a good book about the basics of accounting. It is often available from the library or is quite low cost to buy in paperback or on Kindle.
Low Income Tax Reform Group has a great guide to Trading Allowance and also other tax guides for starting a small business.
Just remember to assess each time if the work you do fits with self employment or if it is really employment. Ad-hoc work is self employment, so occasional weekend babysitting is fine but doing a permanent job for a family wanting you to work every/most weekends would be employment.