Redtail,
I have recently returned from the states, and have worked under the UK CAA system, but am an Australian Licenced Engineer. While the feelings expressed by the others are common with myself, they have not actually addressed your questions, so I shall give it a try.
1. In the UK system (not the Jar66, the BCAR)engineers have to do a detailed company course on an aircraft type, which explains the length of time for one trade. A 5 week course on a modern Airframe alone is not uncommon, but the depth of knowledge required is vastly superior to the requirements of the US operators. They then have to compile a practical work experience schedule on that type, requirements of which may vary from company to company generally, and takes into account the other licences/Authorities already held. They can then apply to the company QA department for issue of a company Authority, which allows them to certify for that type of aircraft and may generally do an oral examination to confirm they know what they are talking about. (I shall not go into detail on limitations to this licence).
The requirements of the A&P can only be judged against the UK LWTR based on relative experience. EG, the LWTR man must sit a number of system based exams, which go into depth on detail (and with exam questions) before he can apply for the Licence Without Type Rating (LWTR), he must also serve a minimum time in the trade for this issue (cannot remember exactly, but think it is 4 years??). Compare that with your FAA requirements. The FAA system requires a company to train the engineer prior to allowing him to sign for the aircraft. I think AA do a 4 week course on the 767, for example, which covers all. While it is much more difficult to get the UK endorsement, with much deeper levels of knowledge required, I have worked with guys in NY that can hold their own anywhere, because they have had many years experience with a particular type. This makes a direct comparison dificult, but generally, the A&P level of knowledge is far below that required for the LWTR. I know people from our system that have passed the A&P, with no study or course, because of our stricter requirements initially. It is only of review level to us.
A fitter is an engineer who does not have a licence and is thus unable to certify for the work of others, or release of the work on the aircraft. Probably akin to someone in the states who works on aeroplanes but does not have an A&P. (EG Overhaul)
As for the schooling side, the engineer can choose to study himself, and sit the basic examinations (LWTR), or if in an airline, when he does his apprenticeship the company may give him training in these fields, but he then has to do the CAA exams himself. However there are approved training schools that offer courses in the specific basic examinations and even run the exams. Most I know in the industry have gone via the airlines or military. I do not know much of the miltaries training system in this regard.
As for the transportability of these company licences (Authorities), most UK airlines recognise other UK airline training, and it is mostly a formality to get the new company authority based on that. However, you can work on any aircraft, but can only sign for work done (by yourself or fitters) on the ones you have the company licence on.
Personally, here in Aus, I have A&C&E&I licences, and it took me some years to get them all, (cannot get interested in Radio) as I sat for the C&E&I myself. I had to do about 35 basic examinations to be able to hold licences in those categories. The depth of knowledge required is the same as the UK.
While I rely on memory for some of this info, hope this is of some help.
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When all else fails, read the manual!