It will be a polarising experience.
Small schools, especially small Preps which were struggling anyway, may well be pushed over the edge. In lots if areas there are too many small Preps for the market, so in free market terms,msome need to close down and Covid may well be the push that makes it happen or causes some schools to merge.
Some smaller schools which also depend on boarders quite heavily might also struggle. It depends if they can fill their paces with UK based students who want to boar and not just be day pupils, becaue boarding is expensive to run unless you achieve a critical mass of numbers to share the not-insubstantial running costs between.
Lots of schools have seen an increase in interest due to disappointment with state school offerings. Whether these translate into higher numbers long term remains to be seen.
Most recession based impacts (and there will be some) tend to be delayed. Most redundancies probably haven't happened yet and are still to come. Most families don't instantly pull their children out but can struggle on for a while and often prioritise educationa nd stability over lots of other expenditures, but this can only go on for so long. Some areas are more subject to such redundancies - places near airports which have lots of pilots etc might struggle a bit with redundancies this time. What you also see is that there is less interest in admissions at the bottom of the school - people are cautious who haven't yet committed to perhaps 7 years of fees and consider more carefully and look more carefully at state options. So competition for places might be a bit less fierce this coming year or two. B this won't really impact schools which are heavily oversubscribed, but feeds down into the less popular schools, which again are often the smaller ones.
I'd expect numbers overall to contract a bit over the next 3 years with a reduction in the number of schools. Some schools won't lose numbers at all, but the number of schools will reduce. In areas of less affluence in particular, independent schools which struggled for numbers (secondary needs a big number to be financially viable and prep schools can be smaller but still need a critical mass of students) will struggle.
Least impacted = big day schools in London and the south-east which were already highly sought after and competitive.
The more features a school has from this list of characteristics, the more tricky it will find things; significant proportion of boarders from overseas, significant numbers boarding form anywhere, low applications per place (or low acceptances in response to offers) previously, areas of lower proportions of professionals, high income, smaller schools, single sex.