Advice(s) needed: relocation to the UK with an autistic child

Hi there! I really need your help to gather as much information as possible.

Here is my case

I have an autistic son (7yo), a really heavy ASD case. Almost non-verbal (tens of words, couple of phrases). Can't serve himself. We live in eastern Europe.

We are attending ~15-20hrs of ABA therapy from the age of one and a half. This autumn we planned to try to put our son in a special school near our home, at least for a couple hours per day.

Now I have an offer to London. Really good one. And I have no idea about what I'll be able to provide for my son in the UK.

I've found some information from Google, but it's very fragmented and I can't build the whole picture.

1) As I understood, first of all, we'll need to have a local autism assessment in the UK. And government-based autism assessment could take up to several years.

Is this correct? Is it possible to pay for a private, paid, but fast autism assessment? Will it be equal to the government-based one?

2) After #1, we'll have to get an ECH plan somewhere. At local authority? Does this mean that different London districts or different cities could give very different ECH plans? How long could it take and how difficult is this process?

3) After getting an ECH plan, we can apply to some school or special school. Here is kind of some impenetrable fog for me :) I don't know anything about UK schooling.

- can we apply to any school? Or probably only to the nearest schools in a place where we will rent something?

- are any of the nearest schools obligated to accept our application?

- basically I even don't know what should we look for: special schools, schools with inclusive classes, or anything else

- I've found several really great-looking special schools for autistic children. How can I understand will I be able to put my kid in some of these schools, will they have classes, are they free or paid, etc, etc. No information about such kind of things on any school site :(

- where the situation with such special schools is better: in London itself, or maybe in small cities around London?

Basically, if I understand correctly, I should aim on some school first, and only then select a place to rent something near this school. But how to select something without all this information?

Any advices are very welcome! And thank you in advance :)

Another questions:

- are there enough ABA services in the UK? How much do they cost?

- how much do nanny services cost in London? Are there "special" nannies available? Like, familiar with special needs, with ABA, etc.