Yeah, I find it very strange why a company like Cex is so slow at their support system. I mean each company is trying to get the majority of users and things like these might change your mind to go elsewhere.
This is by no means unique to cex.io. Pretty much every crypto exchange in existence has problems with poor customer support. It is particularly bad at the moment due to the bull run, increased volume which means increased problems and issues, and them having to process thousands of new accounts. This is what you have to put up with when you use any centralized exchange which takes custody of your coins.
I contacted them through both e-mails, twitter dm's, reddit messages and recently here on their DM.
All you can do now then is to wait. In the meantime, download an open source 2FA app which allows full encrypted back ups so this doesn't happen again.
I have had this problem several times and even changed it to 2Fa via sms which I also had the same problem
SMS is a very insecure method of 2FA and should be avoided where possible.