My daughter was over a year on a waiting for in year admission for Year 2.
I was daily bussing my daughter to her old school in the village we'd left. It couldn't continue as my son was due to start school.
There's a small department within the education team - I've forgotten what they're called now, they don't advertise themselves at all - but they got together and talked with the headmistresses at her old school and the new school because I'd emailed both heads prior and asked if they would consider giving me references/reasons as to why my daughter should 'jump the list', and eventually the new school head took her on, making an extra space in a class limited to 30 normally.
I had been emailing this department constantly though, trying to explain I couldn't afford the bus fares daily and the dilemma when my new son started achool meant I couldn't keep my daughter in old school and so on.
I did say I'd have to take her out and home educate in that case. Luckily the old school headmistress didn't like me (we were always late for school so her Ofsted figures were being singlehandedly sabotaged by me, and my daughter is naturally pale which she had a thing about, plus we'd had so many run-ins about me bringing my baby to school plays when siblings werent allowed and so on..so she reported me to social services for child neglect
so that probably helped, I imagine she wanted to get shot of us 
Anyway, we had a need to be allocated outside of usual criteria, so all those unusual factors above got us a place. It was a combination of the head teachers getting together and agreeing, the 'secret team' within the education department, my constant badgering of everyone involved, and no doubt, the 'child neglect' report combined with me threatening to home educate unless she got a place. Perhaps they thought I'd feed her even less greens and meat if she was home all day instead of in a school environment..
Anyway, it worked. It wasn't luck or a space becoming available.
It was digging, investigating, badgering, making the two school heads talk to eachother, and having a genuine need outside of usual allocation requirements.
If you don't have a genuine need, it won't happen.
But are class sizes now increasing due to immigration? It's been a few years since I've been on the education boards so I'm not up to date.