Yes, TC would certainly stipulate this Harry.
TM Refreshers, to be accepted by the TC, must be delivered by a training provider who is approved to deliver the TM-CPC courses, doesn’t matter if that is the CILT or SAEG version of the qualification.
Beware of outfits that cannot demonstrate they meet this criteria, I’ve seen several who create a course with the name of “TM Refresher” but who’s courses would not be likely to be accepted.
Personally, (and contrary to Cav551’s recommendations) I’d suggest “Beware of the big boys” (eg RHA, LUK) they’ll ‘have your eyes out and come back for the sockets’ pricewise (£714 inc VAT for non-members with the RHA offering)
The infamous Beverly Bell (TC turned training provider/compliance supplier) does hers for about £500 for two days; she ran one recently which featured both herself and Nick Denton (who has also stepped down as a TC) I was tempted to book onto that myself, but it was too far away (Sittingbourne, Kent).
Independent providers would be more pocket-friendly at sub £400. The one I would recommend (if I were to do such a thing) retails at £360 inc VAT for a two day course, but I don’t believe you’re anywhere near the north (no canals up here for narrowboats 
) so that would only be an online option for you.
I personally would not choose an online course, not unless it’s just a tick box exercise for you, I think people gain far more from a classroom situation, especially TM Refresher where group discussions are the order of the day. Which incidentally is my reasoning for not limiting yourself to TM Refs that are also DCPC approved, these have timetables (lesson plans) so are IMO less appropriate (plus with non-DCPC approved courses you get better breaks and an earlier finish 
)
Also be aware that the TC categorically does not endorse, approve or otherwise recommend any training provider or any course (there’s a lot of false advertising going around), the TC either accepts, or does not accept, a course.
Format of courses varies massively; TM Refreshers are a purely UK thing, they aren’t stipulated by the EU regs, like the TMCPC course is. As an overview I would expect them to cover: all the TM responsibilities, from gaining the qualification in the first place to managing O-licences online, covering all the industry updates on MOTs, inspections, maintenance providers, systems of monitoring and reporting on tacho hours, VU downloads, WTD, infringements, PMI analysis, especially brake testing analysis, financial standing, audit requirements, maintaining your CPD in a daily/weekly basis… The list goes on and on.
The course I would recommend gives you a shed load of links to download all the documentation to create a “virtual library” of reference material, thousands of pages in volume, including all the important Stat Docs, MIVR, DVSA enforcement sanctions and categorization of defects (which as Cav551 has said has undergone multiple iterations just within the past year alone).
You definitely want to shop around and ask lots of questions before committing to any one provider.