Unions representing staff based in Parliament wrote to the Speaker to push him to reconsider guidance for post-July 19, in which politicians will be encouraged to wear a mask but will not be mandated to have one on.
It will be compulsory, however, for staff on the estate to continue to have to wear a covering after so-called “freedom day” in England.
Officials said the optional guidance for MPs “hints at a failure by the employer to exercise its duty of care to its own employees”.
But in reply to the unions, including GMB and Unite Sir Lindsay wrote: “Your letter queried the (House of Commons) Commission’s ability to mandate the wearing of face coverings by members.
“As you are aware, I have no power to prevent democratically-elected members from coming onto the estate when the House is sitting.
“As such, there is no meaningful way to enforce a requirement on members to wear a face covering.”
The unions had pointed out that Parliament enforces a dress code that allows the Speaker to prevent access to the chamber to an MP dressed inappropriately, which they said could be extended, as a temporary public health measure, to MPs who seek to enter the chamber without a mask.
Sir Lindsay said such a decision to eject an MP on that basis would have to be taken by the House, rather than the Speaker.
“The rules relating to dress do not, as you suggest, allow me to prevent a member from accessing the chamber – which in itself only accounts for a small proportion of a member’s time during the working day,” he said.
“A member who is inappropriately dressed may not be called to speak, or may be asked to withdraw, but the ejection of a member from the chamber is only enforceable by the House itself.”
It comes as Commons Leader Jacob Rees-Mogg said MPs should be able to choose not to wear a face covering if the green benches are empty next week.
The Cabinet minister told MPs: “In this chamber next week… well, looking around now, I think it’d be pretty safe not to be wearing masks – this chamber is not very full.
“If, on the other hand, we were to have a Budget Day special – which I’m not announcing as business – then I think people might feel the closeness, the proximity of the House would make a mask sensible.
“That is something we can decide for ourselves.”
The Conservative politician said fellow MPs would have to “wait and see” whether he personally thought a busy chamber during Prime Minister’s Questions warranted wearing a face mask, with the new guidance set to be in place for next week’s session with Boris Johnson.
Labour leader Sir Keir Starmer is due to ask MPs in his party to keep up the wearing of face masks and social distancing, even when restrictions are lifted next week.