That is a misrepresentation.
Now the demand from trans rights campaigners at the time was a kind of self-id and no panel, but the government knew that wouldn't fly.
So then all the letters to government emphasised that 40% of people who identify as trans don't medically transition and don't intend to, even if they do get a diagnosis. So no medical transition as a requirement became the new demand and a rubber stamp panel was repeatedly asked for (indeed campaigners bitterly complained about how the panels were described as working in the draft bill).
The government was easily convinced of the former but didn't budge on the latter, because they needed the panel to work like that to sell the GRA to the public. It was one of the main selling points after all - giving careful consideration to each application and all of that.
The government knew telling the public that fully intact men could legally change sex wouldn't fly though, so they came up with a clever trick.
They wrote into the Act that you didn't have to transition to receive a GRC, but if you had transitioned, you absolutely had to prove it. As the first hundreds of applicants were almost all fully post-op transsexuals who had transitioned years earlier, this caused quite a few issues. (Because they often didn't have access to their old records, so they struggled getting the evidence.)
So, the panels took their job seriously, but they did not exceed their authority as Burns claims.
This is the relevant section from the law (Section 3, subsections 1 to 3 of the Gender Recognition Act 2004):
(1) An application under section 1(1)(a) must include either—
(a)a report made by a registered medical practitioner practising in the field of gender dysphoria and a report made by another registered medical practitioner (who may, but need not, practise in that field), or
(b)a report made by a [F1registered psychologist] practising in that field and a report made by a registered medical practitioner (who may, but need not, practise in that field).
(2) But subsection (1) is not complied with unless a report required by that subsection and made by—
(a)a registered medical practitioner, or
(b)a [F1registered psychologist], practising in the field of gender dysphoria includes details of the diagnosis of the applicant’s gender dysphoria.
(3)And subsection (1) is not complied with in a case where —
(a) the applicant has undergone or is undergoing treatment for the purpose of modifying sexual characteristics, or
(b) treatment for that purpose has been prescribed or planned for the applicant, unless at least one of the reports required by that subsection includes details of it.