You will probably save something over using state scools as you'll almost certainly be able to buy the uniform 2nd hand,
No, the uniforms are v. expensive with all the straw boaters and berets and woolen blazers. You might be able to get some second hand, but you can't compare it to a sweatshirt and a couple of shirts from Asda.
individual instrument lessons (If required) can be cheaper than outside scool,
not in my experience, the teachers have a monopoly position and charge £££, plus the lessons tend to be 1-to-1, whereas at a state school group lessons, while less effective, are more likely to be offered and are of course cheaper.
with no petrol costs,
why not?
and, IME, trips, which you by no means have to send your DCs on, tend to be cheaper than at state schools,
no
as the independents arrange their holidays so that trips aren't at peak rates. Also the holiday timings mean that you can often take much cheaper holidays yourselves.
yes this is true if you have still money to spend on holidays after all those fees, going in early July or early-December is easily £1k cheaper than it would be in state school holidays.
With two working parents the childcare at private schools can be quite convenient/economical.
I think it is best to assume you just pay the fees and don't save anything and budget on that basis.