Katie Rowley, 36, from Leeds, has taken legal action against the Cabinet Office.
Ms Rowley says the Government has breached obligations to make broadcasts accessible to deaf people under equality legislation.
She wants a “declaration of unlawfulness” and compensation for “injury to feelings”.
Lawyers representing the Cabinet Office say Ms Rowley’s claim should be dismissed.
A judge based in London is overseeing an online trial.
Mr Justice Fordham is considering rival arguments from lawyers representing Ms Rowley and the Cabinet Office.
Barrister Zoe Leventhal, who is leading the Cabinet Office legal team, told the judge that the issue focused on two briefings last year and said it had been resolved.
“The claim is academic and no longer serves any practical purpose,” she said, in a written case summary.
“The defendant has written to the claimant a number of times, most recently on 22 April 2021, highlighting the academic nature of the claim.”
She added: “The defendant’s case is that damages for injury to feelings are not merited here.”
Barrister Catherine Casserley, who is leading Ms Rowley’s legal team, told the judge that there were more than 70,000 deaf people using British Sign Language (BSL) in England.
“Since March 2020 the Government has been delivering certain key information to the public by means of live briefings, including scientific briefings,” she said, in a written case outline.
“The defendant has chosen to meet the needs of BSL users in accessing those briefings not by the provision of a BSL interpreter ‘on platform’, in an inclusive way which enables the interpretation to be in effect repeated whenever the briefing is shown, as is the case in Wales and in Scotland, for example, but by other means.
“The principal means is by having reached an ‘agreement’ with the BBC who provide BSL interpretation ‘in vision’, shown on the BBC News Channel.”
She told the judge that the issue was “ongoing” and said since the two briefings, in September and October, on which the claim focused there had been a number of further briefings where arrangements “have broken down”.
Miss Casserley said Ms Rowley argued that the Government had failed to meet accessibility obligations under equality legislation.
She added: “By way of final relief the claimant seeks a declaration of unlawfulness and a mandatory order that the defendant provide an on platform interpreter. The claimant also seeks compensation for injury to feelings.”
Miss Casserley said Ms Rowley’s claim was supported by the Royal Association of Deaf People.
Ms Rowley appeared at the hearing via an online link. Sign language interpreters also operated at the hearing.
Solicitor Chris Fry, who is representing Ms Rowley, said before the hearing that he was also representing about 350 other deaf people who have made similar claims.
He said those cases were on hold pending the outcome of the Rowley case.