And the Guardian one in the OP as each have slightly different takes and you get little bits of extra detail from each one:
“In a twist to the tale, Sarah Power, who registered her baby daughter at the same register office – with the same registrar – in October last year, had a similar experience.
“The registrar read back all the details correctly – including that our daughter was female – and then asked us to check the spellings of the name,” she said. “We checked the spelling but not the gender, because the registrar had already said it to us correctly.”
“It was only when we got outside the office door that we looked at the certificate and realised that our daughter had been registered as male.”
Power, however, was able to get a new, corrected birth certificate for her daughter after the registrar directed her to a GPO form. The Home Office, however, say this is no longer an option. ‘The local registration service was advised earlier this year not to issue [corrected] certificates in this way,” they said.”