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This has happened to me twice and twice I managed to get it resolved - only after about 5 vodafone visits/chats I might add! With mine it was a security thing that vodafone had out on my account which affects emails coming in. Basically stops them dead as I was receiving none. Ask them if you have secure net on your account and if so to take it off. The agent did this for me and immediately my emails started coming through on mobile data only/4G - no wifi. The first time it happened I was told again that it was because of the security on the phone so it fixed it both times. Hope that helps anyone with this problem as there seems to be many folks experiencing the same thing.
Thanks for the info. Disabling Secure Net has sorted the problem.
After changing mobiles, buying PAYG SIMS and all the other times consuming efforts this fix has worked on my mobile and a work colleague who started a new contract about three weeks ago. As we are both on the same Business Plan it may be that Secure Net is automatically switched on (this was not the case when I renwed my contract in November). It may not be the case with personal contracts. Presumably this is why PAYG SIMs worked?
Thanks once again for the solution.