It is deluded to think that anywhere in London feels liek the country. Even outside London on Boxhill feels a bit like Hampstead Heath, only it is better because you know you are on a hill.
I made the mistake of moving to Sutton, where the urban centres have a look of rural Surrey. The sad thing is that these centres are surrounded by often very drab connurbation.
The problem with these places is that they are a too far from almost anywhere you might want ot get to, the traffic is appallling and most of the trains are slow.
The best options though are, if you can afford them
Richmond
Kingston
where you are near a lot of open land-not countyrside but Richmond Park has deer and it is joined to Wimbledon Common and other spaces.
Otherwise, to go to North East London, yo can get out into the countyside easily, thre is a lot of open space and it is chepaer than Richmond. The countryside is boring though.
If you wanted to feel a long way from London but still have a 20 minute train ride in to the centre, go to St Albans.