Conservative MP for Romford Andrew Rosindell was appalled by his "inappropriate" remark and asked Mr O'Leary to withdraw the comments.
In response, the 53-year old businessman said he "would happily apologise" and insisted he did not mean to convey "any discourtesy" to the Queen.
He added: "I happily apologise for my opening remarks. It is always hard to judge the room. It normally is a joke that works quite well and I thought it might work well here."