Getting married in Japan...

My partner and I are planning on getting married in Japan, but I don't really know where to begin! We want a small ceremony - either with a few family members or just the two of us. I'm not keen on the idea of getting married in a hotel but like the idea of getting married in a shrine or garden in or around Kyoto or Tokyo, but how do I go about arranging something like that? I am aware that to get married officially it just involves filling in forms, so we may get married in the UK (where we both live) and have a ceremony in Japan. Any ideas?
Thanks!

I had a Shinto ceremony after my marriage and I enjoyed it immensely. There are probably companies around that organize this for foreign visitors, but I don't know of any.

We organized it ourselves and it wasn't too difficult. First you pick a Shrine that you like or where they speak English and you book a date. Note they often are booked solid for months already. Most of the time there are different levels of ceremony you can pick, so you'll need to decide on that (with or without dance, sake ceremony, etc). Then you need to rent a wedding kimono for the both of you. If either of you is taller than 1.80 (6'), it might take some time to find a fitting kimono.
Check with the shrine if they have a party room for hire, it is probably a more interesting place to eat some sushi with your friends and family after the ceremony than renting a similar room at hotel, for instance.
During the ceremony you need to read out a text together, make sure somebody translates it to roman script assuming you don't read kanji.