Katie Rowley, who is in her 30s and 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”.
A judge based in London oversaw an online trial earlier this year.
Mr Justice Fordham is scheduled to deliver a ruling on Wednesday.
Lawyers representing her say she should get several thousand pounds and say the case has implications for other deaf people.
Ministers dispute her claim and lawyers representing the Cabinet Office told the judge that Ms Rowley’s claim should be dismissed.