Well I'm no Kirsty (or Phil lol) but the thing that strikes me from your post is whether you have ever tried out living somewhere really rural (it sounds a bit like you and DH have both always lived in towns or London), and whether you are really really sure this is what you want? I wouldn't stay where you are just for the sake of it but I would do some very careful thinking about what you really want to get out of the move before leaping in as buying/selling houses is an expensive business so you really want to be able to stay where you next move to in at least the medium term - at the moment you have time on your side as your DC won't be starting school for a while, so perhaps an idea would be to rent for a while in the area you choose to see if you really like it, before committing by buying?
Living in the deep countryside can be lovely of course but don't underestimate how much of an adjustment it is if you never have before, especially in winter. I'm like you, our family love outdoor activities, walks, peace and quiet etc., but we could never, ever live really rurally. The inconveniences of having to drive everywhere (meaning children, teenagers or non drivers are trapped and reliant on lifts), often on really bad roads not gritted in winter or lit, 30 minute or more drive to the supermarket so you can only go once a week, no local shops, not being able to get deliveries, takeaways, tradesmen in, the insularity of many country villages meaning its hard to make friends and yet, on the other hand, the nosiness of everyone being into everyone else's business, it can be hard. As you have young children I wonder if you would miss all the opportunities for groups, socialisation etc you get in a town, and if you aren't able to see family and friends easily this could lead to you feeling really isolated. Plus don't underestimate how much maintenance 'land' (or even a large garden) takes (and if you go for the beautiful period house they can also require ++++ maintenance), this could significantly impact on your family time and become a total chore/drag unless mowing lawns, cutting hedges and doing fencing etc for hours on end is a hobby you/DH genuinely enjoy - you can get gardeners/tradesmen in of course but again if you are really rural this can be struggle and costly...
I don't say all this just to put you off, it would all be worth it and more of course if you really love being in the countryside and the rural lifestyle with land is your dream, but for me (and I suspect many others) we can get our countryside fix at the weekends by travelling to open spaces, parks, beaches etc, and retreat to our comfortable and convenient 'town' bubble the rest of the time. I might be wrong but sounds a bit as though if you could have more space (and parking, lol, Kirsty would tell you off for that, no-one should care about parking don't you know!) and easier access to family where you are now, you'd stay, which to me says maybe you would be better off looking at market towns and large villages on the side of London which is closer to your family? yes Kent has some grim bits but then so do Norfolk, Suffolk etc - and there are some lovely small towns and villages where you could probably get a nice detached house and garden in somewhere like Kent, Hampshire, East Sussex, without having to live in the middle of nowhere. Perhaps if you post your budget and wish list over on the Property and DIY board you could get some suggestions?