I am not a childminder but I can answer some of your questions.
Sutton has some basic info available: www.sutton.gov.uk/info/200243/childcare/558/working_in_childcare/2
They say to contact Family Information Service for details about training and cost.
Insurance? You will need Public Liability insurance suitable for childminding. You will need suitable car insurance if you use a car to transport children in your care. You will need to check if your home insurance has any conditions or need changing, as the risk level changes.
Morton Michel and PACEY provide insurance for childminders.
Ofsted? How long will they take? As long as they like! You need to obtain Enhanced DBS checks (on the DBS Update service) on all household members aged 16+, that can take from a few days to many months. You then need to apply to Ofsted as a childminder, that has a 12 week target time but it can take longer.
DBS check £52.10 each, if you know someone who can check your ID.
DBS Update, £13 annual fee, per person.
See more details at: ofsteddbsapplication.co.uk/faq
Ofsted fee is £35
You need a Health Declaration check, which your GP will charge a private fee, this can vary £50-£120 is a typical range. Ask your GP surgery. Not sure if each adult needs that or not... I think it is just the registered person, though Ofsted may request others do it as well.
You need Paediatric First Aid, 12-hour course. This varies in cost, it can be £120 or more in some locations. Your local authority may run courses.
Taxation
As a registered childminder you run your own business. You would register with HMRC as a sole trader and complete a self assessment tax return. You would need to keep accounts - Cash Basis is the easiest method.
also various videos available about self assessment
www.youtube.com/playlist?list=PL8EcnheDt1ziQSjJNRITtCf7XD_ne-_lQ
HMRC Online Training for Childminders
As someone who is self employed, you pay income tax and national insurance on your business profits. National Insurance rates for the self employed.
Pension - you would need to setup your own, such as with NEST Pensions.
Other things:
You may need to do Safeguarding Children training, depending on what you have done at school.
You may need to do Food Hygiene training.
You may need planning permission (not usual though if you care for lots of children your local authority could insist on it).
You will need to register with the ICO, as you will use a camera and hold data about your clients and their children.
With two children yourself who are under age 8, you will be limited to caring for four children under age 8 (6 under 8's in total). Space will also be a factor - refer to EYFS for space requirements. You need to also think about transportation, how you will do a school collection.
Talk to local people - is there demand in your area, in particular demand from parents of children attending the school your 7 year old attends?
Look at information on the PACEY website and contact your local authority Family Information Service who will probably direct you to a briefing session at which you will find out more about what the local authority provides and other training providers.
Hope that helps... I'm sure some childminders will be along at some point to correct anything I have got wrong and add to this list.