With the expenses thing, my guess is I doubt Mr HB is greedy but just desperate because she's trying to live a lifestyle that is actually unaffordable and he can't say no / won't say no, so is claiming things out of desperation to keep the finances up - of course still doesn't justify it.
I've always wondered why they spend a fortune on private school. Tunbridge Wells has some of the best state schools in the country with their Grammars, so it just shows they're not going there for their education but for status. The fees are a combined £40k / year for the twins + additional costs on top so it's probably £45k / year. If it's being funded from a trust fund set up by some family members then it'll be OK, but if they've got to fund themselves it's a huge chunk of change.
I think they have a mortgage?? Anyone I've met with a very big house who has a sizable mortgage and doesn't own their own substantial business, I know they are terrible with money, because they are months from ruin if they lose their current job. The maintenance costs on a big house are obscene as well (and good luck ever getting a trades person to give you a competitive quote when you live in a big house!