Hi Willmum.
I have lost count of how many times I have heard this on the SN boards - parents being told it is 'unlikely they will get a statement' by school staff, HPs etc.
It makes me so angry. Only the LEA can decide this, and the only way you will be on their radar is if you request a statutory assessment of his needs.
You can do this yourself. You do not have to wait for the nursery to do it. Look on the IPSEA website at the model letter for SA requests. Of course it helps if the nursery are on your side. You should tell them you plan to request an assessment (or just request it, and tell them you have already done it), and encourage them to support you (they will be asked to submit their view of the situation). However, do not be put off if they do not share your view.
In addition, if you believe your child needs a diagnosis, push for it. A diagnosis definitely helps to chivvy the LEA along re: SAs, but in no way should you accept a hold up in diagnosis as a reason for refusal to assess. If the LEA do refuse to assess, you can appeal. Many, many LEAs will turn down first applications for SA as a matter of course, actually. Do not let this put you off.
Re: diagnosis. have you seen a Paediatrician? We went all around the houses (CAMHS, SALT, OT, Paed etc), which in a way was helpful as it means we built up a file full of reports detailing DS's issues, however, it was only when I started firing off angry emails and insisting on a diagnosis that the Paed finally brought forrwad our appointment and diagnosed ASD. And yes, it has opened doors. The LEA are assessing and interim funding has been released to provide extra support for my son (he is in reception).
In terms of who to send your request for assessment to - it is usually the chief education office or Head of the SEN Performance Team at your LEA. Look at their website or give them a ring.
Any evidence you can compile is a good thing. Professional reports, medical records, nursery records etc. Start taking notes of all meetings / conversations you have with nursery staff and professionals - you may need this as back up in future.
Sorry, I am also a bitter old hag about the whole statementing process