iCloud services not working over wifi

Problem: iCloud services on all my devices (iPad, iPhone, Macbook Air) not working over my home wifi network after an attempt to reinstall a backup from Time Capsule to iMac. If I want to get my iCloud mail I can only do so by using my cellular network on the phone and sharing it with other devices. When looking into iCloud section in iPhone Settings I get the following message "Verification failed The connection to iCloud Times Out."

Background. Using IOS 8.03 on iPhone 6 Plus and on iPad mini. Using OSX10.10.3 on iMac 27" 2013 & on Macbook Air (13", 2011) + Time Capsule.

Problem started after I experienced difficulties logging into iMac (was getting prohibited symbol on grey Screen.) Apple support talked me through erasing the disk, reinstalling OS X and then reinstalling data from backup on Time Capsule. Went through all that and it made no difference. iMac has since been taken into service centre for repair.

Subsequent to the attempt to repair the iMac iCloud services stopped working over my wifi network. Other aspects of wifi are working; i.e. I can use browser to surf the web, can make Skype calls etc. The only problem seems to be with iCloud related services. Mail takes forever to download e mails and if it does success only the headings and not the content. When I disconnect from the wifi network on the phone and use cellular the e mail comes down fine.

Called Apple Support about this and they seem a bit lost. I tried logging out of iCloud on all my devices (except iMac which is in for repair.) This was very difficult and took a long time but succeeded in the end. Then tried to log back in one by one. Could only do so using cellular network. But once logged back in problem remains.

Also tried restarting Time Capsule with Airport Utility a few times. Makes no difference.

Now stuck for ideas about what to try next. Any suggestions?