Probably not what you want to hear, but please bear in mind also all the downsides of moving to Surrey / Hampshire.
First of all, this is the only country I have seen where everyone will try to convince you that wherever they live is best. You will not find anyone who ever says "this place isn't great but it's all I could afford", let alone anyone saying "actually, I hate it here, moving here was a mistake". No, they are all incredibly happy, they have never looked back, best decision ever, all of them. So do not expect honest feedback from people living there (this applies to the whole of England, not just Surrey).
It is also the only country I have ever seen where people blatantly lie about their commute time. I have plenty of colleagues acquaintances etc who live 20 miles farther away than me but mysteriously take the same time as me, if not less, to get to the office. This never stops cracking me up.
A train journey may be 30 minutes, but what is the door to door time and what if there is a delay? If your train gets cancelled, and the next train, which was supposed to be 25 minutes later, is 20 minutes late, you have added an hour to your commute. If this happens a couple of times a week, you'll lose the will to live.
Most such towns have a train station far from the city centre; commuters need to keep a car just for the 2 to 4 mile journey to the station, and pay for the exorbitant train station parking fee (easily a grand or more a year).
It is all very car centric; in London you can (or you could pre covid...) walk cycle take the train etc to many more areas; in those towns you need the car for pretty much anything. Teenage kids often resent the move to those places for this very reason.
Proximity to the A3 the M25 etc means air quality isn't that much better than in London.
Not all, but many families choosing this lifestyle are white upper middle class families where the husband does the hunter gatherer thing and the wife is a stay at home mum. There tends to be very little diversity in these communities. Dads living in Surrey are more likely to only see their kids at weekends than dads living in Putney.
Is your husband sure he can go to the office just 2-3 days a week? What if next year he is required to go almost always? What if he changes job and his new employer wants him in the office more?
You get a bigger house but also fewer opportunities for social interaction. You won't bump into other families while taking the kids to the park etc.
Have you factored in the cost of the commute and of probably requiring a second car? Over the years it adds up.
Of course everyone is different - I don't like those areas but plenty of people do. I have no interest in convincing you of anything - just pointing out that all these factors need to be considered, too, even if you reach a different conclusion.