Ok, so you are now in the 'make a case for assessment' phase.
They will send you a pack with information about their obligations, and ask you to give an account of why you think your DSs need assessment.
Note that this is not your 'what do they need and why' (that comes later) - more 'why do we need to do something for them; why can't the school cope? Can you prove it?'
In mine, I gave a background to DD1's situation - basically a synopsis of birth-preschool highlighting concerns and what had/hadn't been done. Leading up to the moment Preschool raised their concerns & we were seen at the hospital.
I then gave an outline of DD1's 'present difficulties', breaking into bullet points for each area of development. So for DD1 that was Gross motor, fine motor, social, sleep, speech/language, attention/concentration, sensory issues, obsessions, behaviour, medical condition.
I then did a section called 'considerations for assessment', which gave my opinion on DD1's SEN and the need for additional support. Basically, making it clear that DD1 was not making sufficient progress, even with the 1:1 provided by preschool, that she would need extensive help at school, that her safety would be compromised without a Statement, etc.
I also sent in 18 reports (basically everything I had) as additional evidence, and listed them at the end of my report, so that even if they lost the reports, they couldn't deny that I had submitted them.
It sounds a lot, but the whole thing was about 5 pages.
Then the wait begins, and around 4 weeks later, they will write to you and let you know if they will assess or not.
Once they decide to assess, you will be asked for a fuller assessment of your DSs needs - mine ran to 17 pages in the end.
They will then look at the evidence and either issue a proposed statement, or a 'note in lieu' (a letter telling you why they aren't statementing).
For DD1, I sent the initial letter on September 1st, and got the Final Statement on January 20th - it was quick because they decided on special school and we agreed, so no need for negotiations and the like.