Oscar-winner Redmayne, 34, was awarded an OBE for services to drama, and described it as "an extraordinary thing".
"It is something that I had never thought of and it was never in my wildest imagination."
"It was absolutely wonderful. Also being with such extraordinary people the whole experience is incredibly humbling and also getting to be in Windsor Castle is breathtaking, around Christmas as well with all the decorations."
Redmayne was named in the Queen's Birthday Honours list in June 2015, the same year he won an Academy Award for his portrayal of Professor Stephen Hawking in The Theory Of Everything.
British astronaut Major Peake, 44, received the Companion of the Order of St Michael and St George.
Major Peake, who has been recognised for services to space research and scientific education, became the first British person to walk in space on January 15.
The astronaut set another record when he became the first person to be named in the Queen's Birthday Honours while in space.
He was aboard the International Space Station when he received the call informing him of his recommendation for his award.
Eight days before returning to earth in June, he dedicated the accolade to those who had made his mission possible.
Other honours recipients included Chelsea Ladies manager, Emma Hayes, who was awarded an MBE, and said it was "an unbelievable experience".
Visibly emotional as she described receiving the accolade, she said: "You come here and see the place and the Queen was here - I feel truly humbled."
Hayes also revealed the Queen told her she cannot believe how popular women's football is becoming and encouraged her to "keep inspiring a generation" of girls.