You might find
this website useful. I was researching an answer when I came across it. Otherwise the CAA website seems to be saying that CAA International now run all their exams, including electronically, which would the the far end of a self-study programme.
Perhaps someone with more up-to-date knowledge can advise!
By the way,
at least until recently there were two ways to study for and get a Part 66 AME licence.
Route 1 is an approved course, full-time, (1.5 - 2 years for B1.1) at a Part 147 MTO with that course in its capability. This course includes Practical Training and OJT, run by the MTO or under its direction. If no-one is offering B3, that's probably due to lack of demand and (in my experience) an obstructive, uninterested and ignorant UK CAA).
Route 2 is the self study route. You can take each Module separately, within a time limit to complete them all, until you have a Pass in the ones you need. (See Part 66 syllabus). You can sit the Module exams with the CAA, probably electronically (ie at a proctored centre, using a central question bank). That's where unapproved courses, such as LBP, can give you the study material and tuition that you need.
The difference, with B1.1 and I guess B3, is that Route 2 required a substantially longer work experience period than Route 1. On the other hand, you can be doing that work while studying for and passing the Modules. This is where military/other experience may help, so long as it is relevant to B3 tasks.