I can't see any reason why there'd been an explosion of Annas due to Frozen. It's a child's film and it's children who are obsessed with it so unless it's the children naming the babies adults won't think to use the name any more than they did before.
I really like Anna. I also like Clara and Maisie from your shortlist.
Other ideas:
Amy, April, Astrid, Amber, Anya, Bethan, Charlotte, Chloe, Carys, Cerys, Daisy, Erin, Esme, Edith, Eva, Flora, Freya, Gemma, Hannah, Holly, Halle, Heidi, Hazel, Iris, Ivy, Isla, Jasmine, Josie, Katie, Lily, Layla, Leah, Lara, Mary, Mia, Maia, Maya, Molly, Millie, Nina, Nancy, Nora, Nadine, Orla, Phoebe, Pippa, Poppy, Ruby, Rosie, Rosa, Rachel, Sarah, Sorrell, Seren, Sadie, Scarlet, Thea, Tessa, Zoe.