The food must be good to draw clientele like this, and large enough for Pepys and Povy to withdraw to another room for a private talk:
"Thence by appointment to the White Horse Tavern in Lumbard Street, and there dined with my Lord Rutherford, Povy, Mr. Gauden, Creed, and others, and very merry, and after dinner among other things Povy and I withdrew ..."
"From the ‘Change with Mr. Deering and Luellin to the White Horse tavern in Lombard Street, and there dined with them ..." https://www.pepysdiary.com/diary/1664/11/25/
"Thence with Sir. W. Batten and Lord Bruncker to the White Horse in Lumbard Streete to dine with Captain Cocke, ..." https://www.pepysdiary.com/diary/1666/03/08/
If Pepys was suggesting these and other meetings, perhaps he had an ulterior motive:
"... my waterman told me how the mistress of the Beare tavern ... did lately fling herself into the Thames, and drowned herself; which did trouble me the more, when they tell me it was she that did live at the White Horse tavern in Lumbard Streete, which was a most beautiful woman, as most I have seen. " https://www.pepysdiary.com/diary/1667/02/24/