Can other people access my account?

Only with your express permission. Nobody at Keep Secure can open your box, your key to your box is unique and is for the sole use of the account holder.
You can however nominate one other person to have access to your safety deposit box. You will still only be issued with one unique key, however it does mean that, until any further notification from yourself, the principle keyholder, either one of you can access the vault and if you have brought along the key will be access your safety deposit box.