I don't know about the views of the Queen herself, but I'm interested in Elizabeth II's relatively obscure ancestors. I've done some research on the ancestry of Caroline Louisa Burnaby (1832-1918), the Queen's matrilineal great-grandmother. Caroline's known great-great-great-grandfathers include a carpenter and a baker, and another may have been a husbandman. Caroline also has many more prominent ancestors. She may have traceable royal ancestry, though her descent from Edward I through Philippa (Brooke) (Calverley) Burton given in "Burke's Landed Gentry" is in error, because Elizabeth Burton (bur 1699), wife of Hugh Burnaby, was a daughter of Andrew and Anne (Fairmeadow) Burton of Oakham, co. Rutland, and not of Sir Thomas and Philippa (Brooke) (Calverley) Burton of Stockerston, Leicestershire (see Harleian Society volume 73, the 1681-82 visitation of Rutland).
I haven't looked at John and Elizabeth Walsh much. Wagner's article "Some of the Sixty-four Ancestors of Her Majesty the Queen" in "The Genealogists' Magazine", Mar 1940, pp7-13, gives John Walsh and Elizabeth only as possibilities for the parents of Mary Elizabeth (Walsh) Carpenter, noting that they were witnesses at her marriage in 1779. Gerald Paget's "The Lineage and Ancestry of HRH Prince Charles, Prince of Wales" lists John and Elizabeth without any caveat. An extracted entry in the IGI gives the baptism of a Mary Elizabeth Walsh, daughter of John and Elizabeth, in 1758 at St. Luke, Chelsea.