Being accompanied by a work colleague or trade union rep to any meeting to discuss your request is no longer a formal statutory right. Even so, the Acas Code of Practice on handling in a reasonable manner requests to work flexibly (PDF, 170kb) says it is 'good practice' to allow this.
It is also sensible, as it is likely to make for more effective decision making if you feel supported in the meeting. You will also be able to concentrate on speaking, knowing that your companion is taking notes and that you will have someone to talk through the issues discussed, after the meeting. Management is likely to be accompanied by someone from HR, and basic fairness suggests that you too should have someone alongside to support you, in order to be able to come away from the meeting feeling that you have been fairly treated.
Your union may well have negotiated a right for you to be accompanied under your employer’s policy.
In any event, your employer should adjust its policy to allow you to be accompanied if you have a disability, or if English is not your first language.
Make sure your companion takes good notes of the meeting.
If you later lodge a grievance over the way your employer has handled your flexible working request (for example because you believe that your employer discriminated against you when deciding your application), you will have a statutory right to be accompanied to that grievance meeting. Although the subject matter of the meeting will involve flexible working, the meeting will concern "the performance of a duty by an employer in relation to a worker" (the duty not to discriminate unlawfully), so you will have a statutory right to be accompanied under Section 10 of the Employment Rights Act 1999.