If you are remarrying and want to take your new spouse's surname, your new marriage certificate is usually sufficient. You do not need a deed poll for that alone. Most organisations will process the name change on the strength of the certificate, the same as for a first marriage. However, remarriage name changes frequently involve more complicated situations where a deed poll is either necessary or by far the easier route.
The most common scenario where a deed poll is needed at remarriage: you are currently using a surname from a previous marriage and you want to move to a name other than your new spouse's birth surname. This includes creating a double-barrelled name combining elements of both your names, adopting an entirely new shared surname, dropping a hyphenated name from a first marriage, or reverting to your maiden name at the same time as taking a new name. In all of these cases, the new marriage certificate alone does not cover the change, and a deed poll is the right document.
A deed poll is also useful if you want a single, clean document for all your record updates, rather than presenting both a marriage certificate and a decree absolute (or dissolution order) together and explaining the sequence of events to each organisation. Particularly if you have been through a divorce and a remarriage, a deed poll stating your current name and your intended name is simpler for organisations to process than a stack of certificates.