Welcome Jon,
First thing is that you need to make an appointment at the British Embassy these days before you can get your CNI changed to a local one. Once you have this, you have to take it to the municiple building in your fiancee's area where it takes 10 days for a local posting and process. During this time you will have to attend a pre-wedding cemonar which can take a half day, but you might be able to swing that one if you have been married before (we did anyway) but it is a formality.
I dont think there is any way of making this process faster unless you can fork out big under the table lumps of cash to the right person. Leaving just a week and a bit for the process is (imo) not achievable. But you are there for 4 weeks, so if you get all done as soon as you arrive, I think no problem.
Good luck and have a great time.
