Others have commented about the money, I will just add that the teaching profession is not the best paid (compared to lets say Germany)...

The South East normally includes London, Surrey, Kent, West & East Sussex, Berkshire and perhaps Hampshire.

The differences in housing prices are quite big, and this should help inform your decision. London in general is more expensive (North West, West and Central London the worst, East and South London more affordable in general) , in Surrey the corridor along the train line from London Waterloo to Portsmouth Harbour is also more expensive (towns like Weybridge, Walton on Thames, Woking, Guildford and so on).

Some other people have pointed out websites were you can check this, once you have an idea of the place where you would work and live, people here could comment about the suitability of the area. Keep in mind that most towns will have housing suitable for different incomes. In Woking there are houses for the super rich or for young professionals and also social housing, so most likely you wioll always find housing you can afford close to your place of work.