Having chopped down several dead trees, we've decided we'd like to plant an apple tree. Any advice about where to get one, what to get (eating, not cooking) how/when to plant etc (we are enthusiastic, but ignorant gardeners, having lived in flats for many years). We have a SE facing garden in the warm, wet corner of the country. Thank you very much!
Now is a good time to plant an apple tree. There is lots of advice on the Royal Horticultural Society website here. You need to think about how much space you have (as that will dictate what rootstock the tree is on and therefore its eventual size). If you are short of space, it's pretty easy to espalier a tree against a wall or fence and there are even stepover trees with which you can edge a path. More advice about this - inclduing some suggestions for varieties - here.
I misread your post and thought you were in SE England, in which case I would have heartily recommended going to Brogdale, where you can see dozens of varieities.
If you have the fence space you could look at espalier training more than one tree against a boundary. I have been able to fit 3 apple trees as well as 3 peaches and 2 pears into a 10m by 10m garden. They are all round the edge of the garden and being on dwarf root stock dont impose at all.