Their appeal coincides with celebrations to mark the 60th anniversary of the Queen's coronation.
The letter reminds her of her coronation oath "to the utmost of my power, [to] maintain the laws of God and the true profession of the Gospel".
There will also be a service of thanksgiving and prayer held outside Buckingham Palace to be joined by Bishop Michael Nazir-Ali.
Members of Youth With A Mission (YWAM) will also be present.
"This promises to be an enjoyable and memorable occasion on the 60th anniversary of Her Majesty's Coronation," said Christian Concern, which has coordinated the letter and service.
Christian Concern is also inviting Christians to pray outside Parliament next week when the Marriage (Same Sex Couples) Bill is debated in the House of Lords.
The times and dates of the prayer gatherings are:
Monday 3 June: 12.00-14.00 as Peers prepare to debate the Bill.
Tuesday 4 June 17.00 -19.00 as Peers prepare to vote on the Bill.
The Bill is expected to meet resistance in the House of Lords. Former Archbishop of Canterbury Lord Carey said on Friday that society should be worried about the "unintended consequences" of legalising gay marriage.
"Once we let go of the exclusivity of a one-man one-woman relationship with procreation linking the generations, they why stop there?" he said.
"If it is about love and commitment, then it is entirely logical to extend marriage to two sisters bringing up children together. If it is merely about love and commitment, then there is nothing illogical about multiple relationships, such as two women and one man."