Hi clairecollett,
Thank you for posting in the forum.
I understand that you are getting an error code 805a8011 on your Nokia Lumia 820 when you try to buy any app in the Store.
I would suggest to perform a hard reset of the phone (put it into factory settings), just to remember to do a backup. More Information you can find here:
http://www.windowsphone.com/en-us/how-to/wp8/basics/back-up-my-stuff
http://www.windowsphone.com/en-us/how-to/wp8/basics/reset-my-phone
It seems to be only solution for this error code. Also, you can try to use other Microsoft account.
Please let us know if it helps to solve your issue.
Thanks for your contribution to the forums!
Kind Regards,