Beefeaters from the Tower of London and Hampton Court Palace are on strike in a row over pensions.
About 120 jewel house wardens and other staff are being moved from final salary pensions to an "inferior" model, the GMB union said.
It said the offer from Historic Royal Palaces (HRP) was not good enough.
But HRP said it had been "generous" and the strike would not have a significant impact on the day-to-day operation of sites.
Staff voted overwhelmingly to support strike action, with a result of 91% after a turnout of 88%. There has already been a previous walkout.
Mick Ainsley, GMB regional organiser, said: "Our members are disappointed to have not reached any agreement with HRP, but their offer was simply not good enough."
He added the offer was put to members last week but it was decided it provided little in comparison to what they were losing.
HRP's chief executive John Barnes said 11% of staff were affected by the changes.
"We believe our last offer to be a generous one, and while we respect the rights of trade union members to take industrial action, we will not be changing our decision to close the Defined Benefit scheme," he said.
"The closure of the scheme enables us to increase employer contributions to pensions for everyone by 2% - an offer that is fundamentally fairer to our entire workforce."