For your budget you'd be looking at one of the more modern town houses with a small garden.

Anything Victorian would be too expensive, unless its a large flat (some of the bigger Victorian properties have been converted into large flats which in terms of square footage are probably similar to a small town house).

SE6 postcodes around Blythe Hill are a bit cheaper, but then you are moving further away from Stillness.

It will be tricky for that budget, there's not a huge amount coming on the market at the moment, not sure why - and prices in this area don't seem to be dropping any.
As Bebei says you may have to look at other schools, all the primary schools in this area are pretty good.

But leafleting might work - good luck!