I own a fire extinguisher servicing and supply company. I have no doubt that members of BAFE will tell you that anyone that isn't a member, is not any good at their job. Personally, I don't think the scheme is effective at doing what it's supposed to which is to ensure the competency of its members. I, and many others will confirm, that they have seen evidence that some of the worst fire extinguisher servicing has been carried out by companies claiming to be members of all sorts of organisations.
I myself within the last couple of weeks have serviced extinguishers previously serviced by "approved" companies where ...a) the internal diptube was actually detached inside the extinguisher and....b) an 11 year old stored pressure powder unit with no evidence of any discharge test or recharge and having the original factory fitted gauge dot still in place.
Unfortunately, those people who are not carrying out the work correctly seem to be able to go home at night and sleep tightly in their beds.
In days gone by, any Tom, Dick or Harry could go out and service fire extinguishers as long as they were "competent". Nowadays, BS 5306 Part3:2009 states that a competent person shall be trained and qualified. At least this gives them the knowledge to do it correctly. Many still don't do it correctly. Many are still not qualified.
In 15 years of running my own business, I've only ever been asked once if we were BAFE registered. When I said no, I was asked whether I was a limited company. When I said no, the customer said that he was therefore quite happy.
Liability insurance is a must including product failure. Professional Indemnity is also a must have if a company charges for the advice it gives.
Finding the right person is a challenge. If it was me looking for a servicing company, I would invite 3 companies round, check their insurances, qualifications and prices and go on gut feeling of the guy himself. No guarantees at the end of the day however.
Hope this helps.
John