The Gender Recognition Act 2004, as currently written, is blatantly incompatible with the Equality Act 2010, Article 8 (right to private life). Under a reasonable interpretation a GRC should be granted with no more than a sworn statement. Self-ID laws in other jurisdictions prove that the government has no justification in requiring further proof, and such requirements violate privacy.
Further, refusal to recognize nonbinary people denies recognition to both intersex and trans nonbinary people who wish to keep their "sex assigned at birth" private.
It is unfortunate that the UK Government refuses to fix these issues and will have to be forced to do so in the European Court of Human Rights.