How many English accents are there in the world?

I doubt whether there is a single source for the number of English accents in the world, even if only including native English speakers. But there is likely to be a very large number. In just England alone, there are many different accent groups, for example the broader distinction between "northern" and "southern" English accents. Further groups can be made down to regional levels, e.g. Cockney, Essex, Norfolk, West Country, Midlands, "Brummie" (meaning, Birmingham, although associated with a Midlands accent), Lancashire (including Manchester), Liverpool (called "Scouse"), various Yorkshire accents, Geordie/Mackem (Newcastle and Sunderland and surrounding areas), and Cumbria. These are quite broad groups, and within them there are even finer accent groups. In answer to your question then - there are likely hundreds, if not thousands, of native English accents.