The Scotland v England clash is taking place at the P&J Live Arena on December 21-22.
Organisers say there has been “a huge surge in demand for tickets” and have released more seats.
The Murray brothers are set to lead the Scotland team against an England line-up featuring British No.1 Dan Evans.
It’s a rare Scottish appearance by the two Grand Slam winners, with Andy Murray scheduled to feature in all three sessions across the two days.
Wednesday evening’s session is completely sold out so extra seating capacity is being added to meet the demand. A small number of tickets are still available for the Tuesday evening and Wednesday afternoon sessions.
“We want as many people to be part of this as possible,” said Jamie Murray, who as well as playing is the tournament director. “Battle of the Brits – Scotland versus England is going to be really special for me and for Andy and hopefully for fans as well and we don’t want anyone to miss out.
“I’m thrilled with how ticket sales are going. It’s been a tough year for so many people and I think everyone is excited be able to look forward to something fun like this.”
The Battle of the Brits series was created by Jamie Murray in response to the lack of tournament tennis during the Covid-19 pandemic.
Tickets are available through Ticketmaster and are priced between £35.45 and £147.95.