If you lose your British passport while in Japan, you will need to:

1. Report the loss to the nearest police station (in Japanese, "keisatsusho"), not at a police box (in Japanese, "koban"). You should get a certificate that you have reported the loss to the police (the certificate is called an "ishitsu butsu todoke juri shomeisho").
The passport may be returned. If no such luck, go on to the next stage:

2. Complete a Lost Passport form and a Passport Application form (both can be downloaded from the British Embassy website - see link on the left).

3. Submit to the British Embassy in Tokyo:
The British Embassy Consular (British Passport) Section
1, Ichibancho, Chiyoda-ku, Tokyo 102-8381
- the forms
- the police report
- 2 identical passport photos
- some evidence of your identity/nationality (your birth certificate if this can be obtained)
- the appropriate fee in Yen, in cash (Emergency passport: Yen 13,320 (roughly equivalent to £ 55.50), 32-page passport: Yen 28,560 (£ 119).

4. According to the British Embassy, once they have the correct documents and fee, it takes an average time of 10 working days to isue a new passport.