We are going to Dubai for 2 years in October and I will be the trailing spouse. I have heard that utility companies will only deal with a man and because I will not have a work visa they won’t deal with me either.

Is this true? If so, how can we get round this problem?

No, not at all.  All the utility companies will deal with you and if the utility is in your husbands name you just need to bring a letter with you from your husband authorising you to do what ever you need to do and a copy of his passport.  The government offices also always have ladies queues which is great as you always get served quicker!