Right, well, it seems to me that it is very common for schools to try and deter you from applying for a statement. Partly because it creates a lot of work for them and will cost them a lot of their SEN budget, partly because quite often they really don't see the full issues your child is having. Being charitable, it may also be that they have seen so few people succeed in getting one that they genuinely do think you've got no chance. This happened to me over and over. My previously very good relationship with the school has come under considerable strain during this process.
However, without that proper assessment you will not know whether they need a statement or not, so they should not be deterring you from applying.
How I started out was by talking to anyone I could find who had experience of the process, both in real life and on MN. I also spent a lot of time reading the websites of SOSSEN and IPSEA, charities that work in this field. All the while I was carefully compiling a big file consisting of every single piece of written information I had about DS, school reports, IEPs, nursery and pre-school records, NHS letters and reports, the whole lot. I also went to a one day workshop on the process run by SOSSEN, which helped me understand the process much better. However I still was not convinced DS would get a statement, far from it. He was coping OK with school, no bad behaviour, no refusing to go in, making progress and was getting help form the SALT and OT services. However I did know that I would have to do it by Year 5 if I wanted anything in place for secondary.
What finally spurred me into action was him getting discharged by the OT service at the end of Year 4 (he has AS and dyspraxia). I was sufficiently concerned that I consulted a private OT who basically spent half an hour with him informally and told me to get my application in. At around the same time a comment I read on a forum made me think that, yes, DS did fit the criteria. So in went my application in Jan last year.
It has been very hard, I won't pretend otherwise. I have a part time job for 10 hours a week and at times this process has taken up much more of my time than that. OTOH there have been weks and weeks where nothing happens too. It has also cost me a lot of money having private assessments made. It has been hard logistically keeping on top of the paperwork and meetings, hard emotionally reading the reports that highlight all the most severe problems your child has, hard knowing where to turn when things weren't going to plan. I ended up instructing a solicitor, who has been little short of a miracle worker, but again, at a cost. However, I am now within touching distance of a fully funded place at an independent special school for Year 7, with properly specified and quantified provision. ALthough I've had to appeal twice, I have not yet had to go to a tribunal, it is likely that my current appeal will be resolved without one now. It still could go wrong, I don't want to tempt fate. But if it does I will fight on and I will know that I have done everything in my power to help DS.