Be aware that as far as the UK is concerned there is NO LEGAL requirement for a woman to change her name on marriage. So if you want to wait until the passport is due for renewal, or indeed leave it in your maiden name, there is no problem.
Just in passing. There is no law in UK which says that a woman on marriage must change her name, and in fact, there is no law which even says she can. It is just common practice.
Generally in UK, if there is no law to say you cannot do something then you can do it.
In UK you can change your name by Common Law, i.e. not a written law, (providing it is not for a criminal purpose) and without any requirement to 'confirm it' in law. I did just that 30 years ago, and changed my existing UK passport to my new name. I have since taken up my right to Irish nationality and have a passport in my new name. My Filipino wife has her Filipino passport with a hyphenated surname, her maiden surname and my (new) surname.