Here in the UK (unlike in many other countries) anyone is free to use whatever name they like (as long as there's no intent to commit fraud). You can legally call yourself Alice Smith today, Jane Parker tomorrow, Queen Mars Bar on Tuesday morning, Emperor of the Universe on Tuesday afternoon, and so on. You don't need to change your name by deed poll and (again, as long as there's no intent to commit fraud) you can legally enter into contracts, and sign official documents, in those names.
So, prior to your marriage, you were free to use any name you chose, and to marry under that name. i.e. your marriage certificate is both valid and correct.
As I indicated in my first paragraph, there's not really a 'legal' name for anyone in this country. However, in order to prevent ID theft and fraud, 'officialdom' expects you to have an 'official' name. (It's not a legal requirement; it just simplifies things a great deal for everyone!).
In particular, HM Passport Office staff need to be able to link an applicant's current name to that on their birth certificate. For example, Mrs Mary Smith might apply for a passport but submit a birth certificate in the name of Mary Jones. In order to prove that she's the same person, she needs to submit her marriage certificate, to show when her name was changed.
So the answer to your question is that you might encounter some difficulties on the rare occasions that you need to produce your birth certificate to 'officialdom', because you can't show that the certificate relates to you, but otherwise you're completely 'legal'.
If you've somehow managed to get a passport already (or you're sure that you'll never want one), there's probably no need to do anything unless you can think of anyone else who might require to see your birth certificate.
Otherwise you probably need to see a solicitor, as it's likely that someone who knew you as a child will need to sign an affidavit to show that the person named on your birth certificate and the person named on your marriage certificate are one and the same. (If your mother is still alive, then she would be the obvious person to do so).
Chris