I'm a fan of classic but not posh names.
For me, posh names often end in A, so things like:
Arabella, Araminta, Antonia, Octavia, Henrietta and Cordelia
Lucinda (but not Lucy)
Georgiana/Georgina, but not Georgia
Isabella, Francesca, Olivia and Sophia (but not Isobel, Frances, Olive or Sophie) used to be posh, but not any more as they are so popular
Amanda may have been posh, but was very popular in the 70s when I was a teenager so I don't think of it as at all posh.
Ancient Greek names also used to be posh (eg Antigone, Persephone, Hermione) but are probably now too popular to be.
Alexandra, Victoria, Fiona, Diana, Julia and Maria are on the cusp between classic and posh.
Other classic names:
Elizabeth, Margaret, Mary, Sarah, Catherine, Helen/Helena, Caroline, Rose, Anne/Anna, Jane, Eleanor, Rebecca, Rachel/Rachael, Charlotte, Emma/Emily, Laura, Isobel/Isabel, Lucy, Alice and Frances.