HF training does not have to be provided by a Part 147-approved organisation. It was envisaged, rather short-sightedly, that the training would be carried out by Part 145-approved MROs and the the QAM would ensure that it followed the requirements of Part 145.A.30(e), with the AMC and GM.
If you buy training that is not provided within an MRO, ie by an independent company, as most contractors have to do, you should make sure that their course is approved by the industry and is reputable and properly done. Igonore cheap courses that take less time than is needed to get the material across; most QAMs can recognise this a mile off and some providers are blacklisted.
LRTT offer good courses as the post above says, and
Bostonair Technical Training do the same in Bristol with Refresher courses every other Friday and Initial courses about once a month at weekends. They throw in Fuel Tank Safety L1 as an option.