Hi,
I'm an admissions tutor for computing-related MSc programmes, but once upon a time I ran a software house, and I've employed quite a lot of people who became (good) programmers via unorthodox routes.
One thing I would say is that in the long run, passion and imagination are key attributes in becoming a good programmer, and not every graduate with a BSc in Computer Science has that. Also, at MSc level, maturity, passion and enthusiasm count way more than many people recognise.Your experience in teaching people English may also help you provide an extra range of skills that will given you an advantage in a computing career - many computer folk can't explain the technology; if you can.. that will bring benefits later.
There are many successful stories of graduates in a generalist/conversion MSc making a great career in CS - I had two programmers work for me who came from conversion MScs, and both now work in the States for the (well known) company that bought me out. Andy and Paul are both great coders.
One thing you might want to consider is whether you want to choose a more focussed MSc programme like City University's eBusiness MSc, which particularly emphasises web technologies, and includes specialist lectures on usability and eCommerce systems [disclosure: I teach on this degree], or a more standard conversion MSc that provides a more open range. If you've got some idea of where you want to end up, this may tip the scales in a particular direction. One advantage of a more focussed one is that [presuming it's relevant to the area you want], it gives you great strength in one domain, which may in fact put you ahead, in that area, of 'standard' CS graduates. There are other courses in specialisms around games, finance, etc.
I hope that helps for now.
All the best,
George