To ask DH to continue to work

Would the move mean your DH can afford to retire?

If he can afford to retire, then you kind of need to go along with it. That’s the problem of being reliant on a man for money, married or not.

Exactly. Then OP says that she does work.

If you tell the truth, you don't need a good memory - Judge Judy

YANBU, selling up and moving a whole family from London into the countryside is a massive decision and a huge change in lifestyle. You all need to be on the same page. Lots of people do it and live to regret the decision because they can’t afford to move back to their previous standard of living.

Talk to your DH and find out more about what he wants and how you might be able to compromise. A weekend place in the country might be an option though it usually becomes a total pain packing up for the weekend and driving through the traffic both ways.

If you live in central London would you be up for a move a bit further out where there is more green space but still within a short commute of the city?

Yes, the crucial bit you've missed out OP is why DH wants to move and what that has to do with his job.

Your current post is summed up as "I like where I live and have a lovely life but DH wants to move and I don't". YANBU to not want to move, but you haven't explained why DH thinks you (the family) should.

It sounds like he is finding being the main earner difficult and you are the the only one happy with the situation at the moment.

You can't sustain your current lifestyle on your wage alone. So there needs to be a chat about moving forwards with a lifestyle that is affordable and happy for you both.

Well you earn the same as him and then you get to decide.

The 'why' is crucial here. Maybe he is burning out and needs the move for mental/physical health issues, maybe there are financial reasons he can't sustain the London house, the private London secondary schools, the open house for friends and relatives from all over the world.
I don't think I would be stamping my size 5s and demanding he continue to fund a lifestyle that would leave him ill, bankrupt or hating all the extended family and friends.
I'd be getting to the bottom of the 'why' and that in itself might throw up some compromise solutions.

Is there a middle ground?

Is your DH’s job funding your current lifestyle, OP? I think you may have implied that but I am not quite sure.

Your DC sound rather young, so I am guessing you haven’t lived in this (lovely sounding!) house all that long. Are mortgage payments significant? If DH’s job is funding tuition for at least 3 private school places (because they ‘all’ attend such) on top of the mortgage, he presumably has a high pressure job.

I believe that you do work hard at your job and as a homemaker in the most profound sense of the word (and that this job, done well, is vastly underrated) but the pressure is not the same. As @InBedBy10 said, a weekend cottage on top of all this does nothing to ease the pressure on DH.

As I understand it, YABU. DH deserves the same chance as you to find life satisfaction. You can stay in London considerably more economically, you can increase your own financial contribution, you can embark on a new way of life. You have lots of agency.

Ah, I cross posted with your latest.
If there is really no mental or physical illness going on then regardless of where you live I don't find it acceptable that one partner unilaterally decides not to work anymore (totally different if it's a joint decisions). But there is still a discussion to be had over where you live. I wouldn't like to think of my dh living somewhere he absolutely hated on my say-so.

Probably the most selfish post I have ever seen.

I think you need to look at the risks. If he is very stressed and unhappy he could become very unwell; and that would have significant impact on the whole family. If you downsize would he potentially retrain or do you have a career that you would like to develop? Maybe accessing some coaching and financial planning could help in terms of working out mutual goals

Your DH is burning out. I’m sure you love him more than your lifestyle. Live in the country (we have private schools there too) and visit London. Your DH deserves to enjoy life too.

him not working doesn't sound viable even if you do move and change schools. he sounds unhappy. are you looking at making changes to try and take on more of the financial pressures? unless there's a backstory, your post suggests that you want your h to put up and shut up so that you can have a lovely lifestyle. how is that fair or sustainable?

If you sell up and move, how long would the money leftover last you if DH doesn’t want to work? Enough to pay school fees and your bills? What about pension?

Really? OP says her DH is fed up of life and doesn't like his job.
That sounds like he is having mental health problems to me.

I agree that he can't unilaterally decide the family is moving, but OP also can't unilaterally decide he must keep working at his (presumably stressful, well paid) job just because she likes the lifestyle it provides.

Sorry, OP, I have just seen your update above.

The man sounds burnt out. Counselling may help, not to persuade him to continue bringing in the big bucks but to help him figure out what he really wants. I assume there is a lot of daylight between his current job and working in a zoo. There is probably a suitable middle ground.

You may need to step up.

There is a middle ground to be found. Something has to change and you know that. I speak as someone who was burning out, I was a in a firm in a niche role in London. Extremely well paid but I was having a breakdown almost every weekend. After a total of 7 years of that, I made a change with DH's support. Less money, better lifestyle. It required big compromises from both of us.

I live in the country and I like it but I would much rather live in London. Sounds like you are at an impasse. He wants to give up work and to do that you have to sell up, you want to stay put but can only do that if he carries on working which he hates. I gave up work at one point because I wanted to potter about. I lasted about ten months and then I was fed up, bored, mildly depressed and fatter. It seemed really attractive until I actually did it. Couldn't get back to work quickly enough. Any chance of him taking a sabbatical from work to see what it's like? May be useful for him to recharge his batteries too.

He's burnt out. You need to listen to him before he gets in a state. For example work towards a higher paid job so your DH can reduce hours a bit.

You're the one that wants the lifestyle but you're expecting him to run himself into the ground to fund it. You need to step up or start making sacrifices to allow him to wind down a bit before he does something drastic and has a breakdown.

Is he retiring or getting a new job?

Kids can still have a good education without private school fees. It sounds like your dh is burnt out.

Your husband's health and wellbeing should be your priority over the vibe of living in London. Maybe you should find a better paying job so that he can get a job with less stress? I don't think him not working again sounds viable but he should be able to get a less stressful job. My DH recently had to do the same because he was getting so ill from work stress and I was terrified he would end up having a heart attack. We had to extend our mortgage and make sacrifices, but I said yes to all of it in a heartbeat because he's far more important to me than any lifestyle. Stop being selfish.