The IMC Rating is nothing to do with EASA and its entry into EASA licences as an IR(R) is no more than an administrative fudge. There is no requirement for the IMC Rating course to be conducted within an ATO, an RTF or a DTO, nor for it to be approved and so there is nothing to prevent a DTO from conducting the training.
A DTO will not be able to conduct training for the BIR in the foreseeable future - Part DTO lists the training that is permitted at a DTO and will take at least 3 years to change. In any case, as any training provided by a UK training organisation after 29 March 2019 will not be accepted for the issue of an EASA licence, rating or certificate, it is unlikely that any training for the BIR will ever take place at any UK-based organisation.