The MCC added that sales were “strong” for the opening two days and also across the rest of their international fixtures this summer, with the one-day international against India sold out.
Broad, 35, has returned to the England squad after being left out of the tour to the West Indies in March.
Whereas his long-time new-ball partner James Anderson said he considered retiring after that omission, Broad insisted he did not think about ending his international career.
“I’m delighted to be in this squad. I was disappointed to miss out on a Test tour, but that’s life,” said Broad, who has taken 537 wickets in 152 Tests.
“I’m very forward focussed, very excited to be here. I’m going in with the mindset to attack each week as hard as I can, leave my heart and soul on the field, and taking myself back to [being] as if I’d played zero Test cricket.”
Broad and Anderson are alongside fellow pace bowlers Craig Overton and Matty Potts in the squad.
All four could play if England decide to omit left-arm spinner Jack Leach. If Leach is selected, it could be that Overton gets the nod because of his superior batting, leaving two places for Broad, Anderson and the uncapped Potts.