I'm very surprised that all of you have trouble with this.
It isn't the law that the wife has to take the husband's surname, therefore there is absolutely no reason why the husband should have any more trouble going double barrelled than the wife.
I would be challenging any company who agreed to change my surname but not my husband's as to why they were so sexist and discriminating my husband because of his gender! It is 2020, not the 1950's!
If you look on the gov site for passports it tells you all you need to know - you or your husband DO NOT need to change your name by deed poll.
www.gov.uk/changing-passport-information/name-marriage-and-civil-partnership
As I said, our experience is very recent (December), and neither of us have had any trouble at all with changing our surnames with any government, financial, legal or any other companies.
I've been married once before, 20 years ago, and the marriage certificate I got from the church had both our maiden names on, as this is the name you use to get married. Nowhere on it does it have your new surname. Has this changed?? 20 years ago my then husband also went double barelled after the marriage, and again, had no problem in obtaining new passport, driving licence etc.
I am not doubting what other posters are saying, however I suggest you look at the .gov site for passport and driving licence where it is very clear.