What is the process/requirement within JCT for getting subcontractors accepted?
There is very little stated in the contract in this regard.
Clause 3.7.1 of the SBC (clause 3.5 of the IBC) prohibits the Contractor from sub-contracting without the Architect’s / Employer’s (if in relation to CDP design) consent however it does state how you seek consent or on what basis it will or will not be given. Breaching this clause though does give the Employer the right to terminate under clause 126.96.36.199 of the SBC (clause 188.8.131.52 of the IBC) so the obligation should not be ignored.
I suggest you write to Architect / Employer advising them who you are intending to sub-contract with and requesting their consent.