I must admit I always come back from visiting people in the SE feeling very grateful for our quality of life / cost of life ratio here. Of course there aren't many of the extremely well-paying jobs that are available in London but, if your DH can transfer in the same job, that sounds ideal.
Nottingham is a lovely place to raise a family. There are some really nice bits and some not very nice bits and some inbetween bits that look very scruffy. Things I think are great are that the town centre is big enough to offer everything you might want in a regional city - theatres, cinemas, galleries, restaurants, shops - while being compact and easy to get around, on foot and with excellent public transport.
Also, it's easy to get to lovely green spaces. Within the suburbs there's Wollaton Park, Attenborough, Colwick Park, Rushcliffe Country Park etc. You can get to pretty villages and countryside in the Wolds to the south, east to Bingham and Southwell and some parts north (stark mixture of pretty agricultural and not-so-pretty ex-mining villages). Then, within 45 mins you can be in the Peak District. The towns to the west are not so lovely but there will be some nice villages (not so familiar with this area).
Obvious areas are West Bridgford, Wollaton, Sherwood, Mapperley, Beeston - Bramcote - Chilwell.
Rushcliffe (West Bridgford and rural south) always comes out extremely well in national 'lovely places to live' ratings. WB is it's own small town and very convenient to the centre of Nottingham too. Not so cheap but probably compares well to London!