There are quite a number of British international schools in Brussels -- I think a good place to start would be to do some research and get in touch directly with any suitable institutions you come across to find out if they have any vacancies.
To get you started, take a look at our page of International Schools in Brussels. Here are a couple of schools you might want to check out, (the page I linked above has a few more): British Junior Academy of Brussels, The British School of Brussels, The British International School of Brussels and St Paul's British Primary School.
Hope that helps! Best of luck.