If it is a limited company, and not a charity, then there are shareholders somewhere looking for a return/profit, or who may choose to sell the school. There may not be a typical governing body etc. Not necessarily a problem, but worth being aware of.
All limited company accounts are available from the Companies House website, though you do need to pay £1 per document I believe.
I appreciate that you are looking for advice on small class dynamics, but actually this is all inter-related, especially in prep schools which don't have a guaranteed supply of pupils. One small year group can be offputting to other potential parents and actually for a school who needs a certain level of income to meet the monthly salary cost, things can quickly spiral downwards. If this is a co-ed school, then in particular it will be difficult to recruit girls into an established single sex year, and obviously if you turn away any parents, you are turning away siblings etc in future years.
Eg one of my dcs current school is full, with the exception of Year 5 (which was a tough boy-heavy and ill disciplined year group which led to several parents withdrawing their children) and Year 3 (the year where you would expect to have the younger siblings of Year 5). As I have said below I'm not worried about the finances of that school, BUT I have checked them, and I know the number of pupils to break even. Prep schools typically run on tight numbers. So with this particular school I know that they have an upper limit of 172 children (the number they can physically fit in) but they need to have at least 153 fee-paying children in order to cover their costs.
With my other child's school I can be more relaxed on number as it is owned as part of a group of schools by a church educational charitable trust. Not only is the attached senior school very oversubscribed, but even if that suffered a financial loss there are reserves across the pool of schools which could support it for a while. But I still look at the accounts. By the way both sets of school accounts disclose the total amounts given in bursaries each year.
In the current economic environment headteachers are expecting astute parents to do their homework, and will have no problem in answering any questions about the school finances. If you always have the option of an excellent state school locally then of course you can take greater risks, but ime it is easier to ask these questions before you have signed up, rather than afterwards. If you don't feel comfortable asking financial questions, then at least make some enquiries as to how many children are in the class above, and how many are registered for the one below (at the very least they should know about siblings). As noted with dc's school, a low intake will have a knock-on typically 2 years below, so provided the intake above and below yours are full it may not be critical.
In small schools sport tends to happen across 2 yeargroups (so team sports would be U9 and U11), so this alone is gives you an opening to ask the question without appearing to question the finances if you felt that you couldn't do that.