In many cases, the 13+ application deadline is up to three years prior to entry, and it’s rare for schools to accommodate latecomers (especially in London).
An increasing number of schools with year 9 entry are using a pre-test in Years 6 or 7 to slim down large numbers of applicants in advance. This is either their own design, or the ISEB Common Pre-test (a list of schools who use this can be found here). The ISEB has been called a ‘pre-pre-test’, as schools like St. Paul’s and Westminster will still conduct their own pre-tests after conducting the ISEB. For a high-ranking London day school, it is common to have upwards of 1,000 candidates sitting for 150 or so places, and the number of applicants continues to rise.
However, for most 11+ entries, you can register during the first term of Year 6. 11+ tends to be a more straightforward process, though there is still variation in the difficulty of this process across different schools. Typically, there are exams in Maths, English, Science and Verbal/Non-verbal Reasoning. These are taken in the January of the Year 6.