seems to indicate that private flights not effected.
Private flights are included, "chargeable" is in reference to APD, not to how the aircraft is operated.
To quote from the HMRC:
A chargeable passenger is anyone carried on a chargeable aircraft irrespective of whether they have paid for their carriage, which is not covered by an exemption.
One thing is the rate that will be charged will be the higher rate,
Careful there, only the higher rate is charged when over 20t, between 5.7t and 20T it is the "standard rate", and over 19pax AND 20t it is the "airline" rate, so refer to pitch and classes.
So a Citation/Hawker/Lear pays less than the heavy metal does.
For the Russian destinations, they left in the break at the Urals, without going into details what the exact boundary is, pretty vague if you ask me.
There are also specific rules for non UK based operators as to admin representatives and paying security (part of your estimated APD) up front.