Speaking in Parliament this morning (Thursday), during the monthly session where MPs can ask questions relevant to the Church, the Conservative MP for Meriden said the Church of England was very concerned by the judgment of the European Court of Justice.
Spellman said the ban: "Conflicts with the pre-existing rulings of the Court of Human Rights.
"Presumably by leaving the European Union, we stand some chance of resolving these inconsistencies."
Last month, judges in the European Court said the banning of any political, philosophical or religious sign in the workplace does not constitute direct discrimination.
The test case regarded the wearing of a Muslim veil in Belgium.
Sir David Amess, Conservative MP for Southend West agreed with Spellman and said Brexit was: "Yet another reason to be pleased that the British people took the decision last year to leave the European Union as the ruling was deeply offensive to people of all faiths and totally unnecessary."
Last month, Prime Minister Theresa May also questioned the European Court's ruling.
Speaking during Prime Minister's Questions, she said: "It's the right of all women to choose how they dress and we don't intend to legislate on this issue.
"There will be times where it's right for a veil to be asked to be removed such as border security or perhaps in courts.
"Individual institutions can make their own policies but it is not for government to tell women what they can or cannot wear and we want to continue that strong tradition of freedom of expression."