Starlight, sadly that's no longer true - not with secondaries that are academies anyway, the only school to name around here are academies and they are refusing to be named for children with statements as a matter of course.
Flowwithit, in our case applying for a statement made things worse, because the school took umbrage at us applying when they said ds didn't need one. They are now not only providing him with less support than he had before, but also lying about it and insisting they are giving him all the support in his statement.
Essentially, what we've learned is that if a school is crap at supporting children with SEN, it's extremely rare for that to change, regardless of what you do. LEAs can only see so much and the system makes it very easy for schools to do the minimum, then lie and falsify records to cover their tracks. 
I have been through the loop of wishing I hadn't applied, but eventually come to the conclusion that it was still the right thing to do. The last three years have been hell, for ds - and for us, but they could have been so much worse if the school hadn't been under constant scrutiny with external professionals coming in and out on a regular basis.
If I could have moved him I would have done, but there is simply nowhere for him to go, there are three primaries to choose from and they all have the same attitude - in fact one of them has a reputation for being much worse.
Unfortunately for us, gaining a statement actually lost ds a place at the local secondary school where the whole of the rest of his school year will be going, because since we applied for the statement, they became and academy and have been really aggressive in creating a 'brand' that does not include children with SEN. They flat out refused to take any pupils with statements in the next intake, but fortunately for us, that's looking like having a positive outcome, as it means the LA can't shove him in any other MS secondary they like either, as they're all pretty much of a muchness in our area. So - nothing definite, but it's looking like he may get an out of area independent placement as a result. Unfortunately for him that means leaving his best friend and small social group and he is devastated about it. 
It's a dilemma and I think we've definitely been unlucky, but on balance I would always advise to apply for a statement if a child's needs cannot be met via the normal school's facilities etc.