According to the CAA website at :
http://www.caa.co.uk/Commercial-industry/Pilot-licences/Training/IR-modular/IR-(A)-modular-course/ (Sorry, you'll have to copy and paste the link as the link structure seems to confuses the Flyer software...
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Basic instrument flight module
This consists of 10 hours of instrument time under instruction, of which up to 5 hours can be instrument ground time in a BITD, FNPT I or II, or an FFS. Once you have completed this you will be issued with a course completion certificate.
Procedural instrument flight module
This consists of the remainder of the training syllabus for the IR(A), 40 hours single engine or 45 hours multi-engine instrument time under instruction and the theoretical knowledge course for the IR(A).
Completing your training
All instructional stages must be completed in one continuous, approved course of training.
That implies that the BIFM course (even though it's covered in the IR(R) anyway) must be 'approved'; ipso facto, it may only be provided by an ATO.
However, I would be delighted to be told that my deduction is incorrect!