In answer to your question, in the order they appear in the list IMO names which are not so much posh as classy and classic and bridge social divides:
Thomas, William, James, George, Joseph, Benjamin, Alexander, Henry, Matthew, Edward, Michael, Charles, Sebastian, David, John, Robert, Christopher, Frederick
Olivia, Emily, Sophie, Grace, Charlotte, Isabella/Isabelle/Isobel, Hannah, Imogen, Emma, Elizabeth, Matilda, Alice, Georgia, Eleanor, Anna, Rebecca, Sarah/Sara, Martha, Alexandra, Harriet, Lydia, Maria
Just IMHO of course.