Science teacher "Besides that, finances haven't altered much in the negative direction for fee-paying parents, as a whole"
How did you reach this conclusion science teacher?!
Of course finances are changing in a negative direction because there is a recession on and people are losing their jobs and fearing that they will lose their jobs, or are retaining their jobs but not getting the bonuses they may have used to pay fees. This includes people who may well have children in private schools such as bankers, and other city workers, people who work in property, people who run businesses whose profits are down etc.
Do you think everyone who sends their child to private school is a teacher or doctor?
These are two of the professions that might not be affected so badly but most other people are affected by the recession.
Not everyone has a mortgage, some people are debt free and have savings. They are not helped by low interest rates. (am not saying low interest rates are a bad thing just explaining why people are not necessarily better off as a result of low interest rates)
As to the effect on private schools. I expect people already in the private sector will try to avoid taking their children out. Maybe the private sector will lose some people who live in areas where there are good state schools. They will maybe delay putting their children in private school from 3/4 and send them later, or send them to grammar schools/good comps instead of private secondary.
I fear private schools will be affected more by the government policy of forcing schools to offer bursaries etc. which will involve fees being raised. This will mean that private education will end up being for the very rich who can afford the higher fees and those on lower salaries with bright kids who can use the bursaries. Middle earning professionals might end up being priced out even more than they are at the moment.