iCloud.com email problem (when using Safari)

Suddenly, I have a major problem when using iCloud.com in Safari. Every time I open a new message window, as soon as type the first letter of any email address in the To: field, iCloud.com closes and I have to sign in again. This occurs whether I'm composing a new message from my iCloud.com email address or my recently added custom domain email address.

If I go to iCloud.com using any other browser than Safari, this does not happen and everything works fine with both email accounts. Also, there is not problem a when using Apple Mail on my Mac, iPad or iPhone. Only when using Safari does this occur.