This is one of those "how long is a piece of string" questions.
A qualified teacher should be able to teach a class of 30 children without any major special needs alone. A TA in most classes, is not a neccessity. The ONLY exception to this is children with statements in mainstream. This is something I think ALL parents should be given more awareness of, given the current austerity climate or schools risk getting flack from the general public for something completely beyond their control.
A lot depends on what the statements specify. Contrary to popular belief a statement may not actually contain ANY TA time at all - I had a lad on teaching practice like this. At the opposite extreme my mother taught kids in a mainstream school that had 2 TA's per child at all times.
School Action has already been explained, and really is no big deal. Kids hop on and off the school action register at various points in their school careers all the time. It's just to flag up additional in-house support and a child may be placed on this if they seem to be falling behind in one subject, or when recovering from an op etc. Or as described above they just need a writing slope and pencil grip.
School Action Plus is the tricky group to quantify as sadly lots of children with this status SHOULD have a statement really but for various reasons don't. These children require the input of resources external to the school such as SALT, or an EP.
In order to get a statement a child's needs have to vary from the norm quite considerably, but there are MANY more forms of educational support than just the use of a TA.
ALNR could just mean children for whom English isn't their first language but who are now at the stage where they just need the odd specialist or scientific word explained to them, so just need a watchful eye kept rather than full on TA support in the classroom iyswim.
If you genuinely feel your child needs more TA time then the only way to guarantee this legally is via the formal statementing process.