The motion was tabled by Mr Baker who has been supported by other MPs from all three parties.
A total of 22 said their 'principal duty' should be to represent the people who voted for them — not the monarch.
They want the Commons and the Lords
to be allowed to swear allegiance to their 'constituents and the nation' instead.
The declaration has been sworn by those joining or returning to Parliament for more than 500 years and MPs and peers must take the oath before they are able to take their seats and draw their salaries.
The wording of the oath, which has changed over the years, currently reads, "I swear by Almighty God that I will be faithful and bear true allegiance to Her Majesty Queen Elizabeth, her heirs and successors, according to law. So help me God."
Atheists are allowed to replace the religious element by saying they 'solemnly, sincerely and truly declare and affirm' their allegiance.
Seaford county councillor Michael Murphy said he was 'angered and disgusted' by the news.
He said, "It all comes down to whether someone has a commitment to this country.
"At the present time, the Queen is the Head of State and, as the Crown, is the embodiment of this nation of ours.
"As such, when swearing allegiance to the Queen, you are swearing allegiance to the Crown, and thence to the country.
"The military, the police and the judiciary all swear allegiance to the Queen as the embodiment of the nation.
"They recognise that they are not just swearing allegiance to an individual, but are expressing their allegiance to this country."
Mr Baker hit back and said he was trying to get MPs 'back in touch with their constituents' and added, "Cllr Murphy cannot see a brick wall without trying to politicise it.
"The reality is this is a sensible suggestion which is supported by all three parties, including his own."
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