2005 is a bit late to look at special school places - a lot were closed in the 90s. I also tried to find numbers last night but didn't manage and then it got too late.
Very very roughly, because I need to take DC out in a minute, the timeline seems to go like this in my understanding. Apologies for any errors as I'm pulling this from memory and haven't fact checked.
~60s/70s > special schools fairly hidden (e.g. most people unaware of this as Blue says), and pretty much unregulated - disabled children may not have been educated at all. Lower ability or difficult to engage pupils not really bothered with, disruptive behaviour discouraged with physical violence/intimidation of pupils by teachers. School leaving age changed to the summer that pupils are 16 in 1972 - previous to this pupils could leave at any of 3 points during the year as long as they had turned 15.
~80s/early 90s > Shift away from physical discipline, questions being raised about the education offered to SEND pupils, aim to raise standards in these areas, but still not a huge amount of standardisation - some teachers still v intimidating/bullying towards pupils even if not officially allowed to physically punish. Towards the mid 90s you see a rise in official permanent exclusions which seems to be a question mark why is this happening/how to tackle this.
~ Mid 90s/00s > More accountability for schools (which meant more paperwork for teachers) - OFSTED, digitalisation/central records mean more focus on issues like truancy. Many special schools closed, inclusion policies and new guidelines about exclusion. It seems this was a very brief "golden age" for services like CAMHS as they experienced more funding. Seems like things like speech therapy and assessments were available to meet demand during this time. More awareness and diagnosis of things like dyslexia, less tolerance of children being left behind. Beginnings of awareness/diagnosis of (what was then) Asperger's Syndrome and ADHD. I get the impression there was positivity during this time about the prospect of inclusion for SEND children in mainstream schools, although this wasn't always shared by teachers who were already struggling with paperwork and expectations from higher up.
~ Late 00s/early 10s > Massive cuts to services due to austerity policies which seemed to start off the "snowball effect" mentioned before. Schools struggling with funding deficits as well as increased expectation to handle children with higher levels of need.
~10s to now ish > Hugely increased demand for services completely overwhelming capacity likely because services have been cut, but also demand increases due to school funding cuts + increased expectations meaning schools are less able to cope with pupil needs/behaviour. Plus parents have more awareness and more likely to push for referral due to information found on social media/parenting forums/wider discussion of these issues in the media.