"Alot of schools in the local area are over subscribed and there are alot of private and grammar schools also in the area too. "
If you're in a city with grammar schools, there will be a lot of people tempted to pay for primary (in order to increase their chances, in their eyes, of getting into the state grammar) and then willing to pay for secondary (to get, again in their eyes, a quasi-grammar). If a private school can't manage to keep its head above water in that environment, you have to ask why. A desire to get into the super-selectives, and a plan-B after not getting into the super-selectives, keeps a surprising number of private schools running in my city. Given the quality of those that do stay in business (OK, but nothing astounding), I'd be sceptical about one that couldn't.
Secondly, almost all private schools are de facto or de jure selective, either on admission or at the "perhaps you might like to consider going elsewhere" parents' evening. Selective schools rarely have the experience, interest or ability to deal with children who are currently low attainers. There are honourable exceptions, but they're rare, and tend to specialise so you'd know if that was its strength. A lot of people who pay for an education want to pay for an imagined 1957 grammar education, all facts and wooden desks and O Levels, and that doesn't tend to sit well with a nurturing approach to bringing the best out of people who are struggling. Building that attention for people who need a little more help takes time.
Thirdly, I'd be very surprised if the admission policy you describe is actually the case. It appears to breach almost every clause of the admissions code. I would suspect that all children who have places at the point of conversion are guaranteed places, but the conversion has already happened. The school secretary is not, with respect, the admissions officer, and free school admissions are handled via the LEA common application form, not directly by the school. There are other threads about admission myths, sometimes spread by schools themselves, and I would be very surprised if what you have been told is in fact correct. I could be wrong.
What meditrina says about the PAN is right, too. It's unlikely that under current funding formulae any school could maintain class sizes like that in the long term, and even if they tried, they would find it very difficult to resist appeals which have the effect of raising the PAN.