What you describe is completely common, people get married, change names, or don't, or have varied naming conventions. ECO's are accustomed to the wide range of possibilities.
You can do exactly what you describe: apply with your current passport in your maiden name, accompanied by your marriage certificate, and all your supporting documentation in your married name.
Your visa will be issued in whatever name is on the passport. You're good to travel on that passport, along with your visa. You want your ticket to match that of the passport on which you'll travel, particularly when you require a visa to enter a country.
Should you decide renew your passport prior to travel, and the new passport contains your married name, you can travel with both passports, and with a certified copy of your marriage certificate (I wouldn't take the original, to be safe, but make sure it's certified).
On arrival, you present your maiden-name passport with visa, your new passport with new name, and your marriage certificate.
In either instance, do remember to fill out any landing information in the name in your visa/passport.
There are global variations to naming conventions and practices, as well as traditions and cultures, and circumstances, in which lineal offspring have surnames different from those of their parents or antecedents. As required, applicants should have an apostille copy of their marriage license and, as appropriate, an accompanying apostille translation.
Refer to the full guidance on UK supporting documents.