Welcome aboard pollyb!
WTFH has listed the best of the major players. I've little experience with most of them, but work at times during the season for Interski. A few of the guys I worked for have been through their nine-week course and been very impressed.
A lot of your decision will probably rest with what you want to do with your qualifications (which, fingers crossed, you will have at the end of the course).
If you'd like to work a bit in Europe and like the idea of climbing the instructor hierarchy, then BASI is probably the way to go - as part of the 'Eurozone' group of countries (nothing to do with the EU), they are much more inter-compatible with the other countries (such as France - arguably one of the most difficult places to work as an instructor).
If you just want the experience, and possibly a bit of temporary work each season for a week or two of paid skiing, then you needn't limit yourself to BASI (as they have a bit of a reputation for providing poor support for their instructors once they have their money, they are also very expensive, and, outside of the package courses it can be a real pain to get all the little courses completed to pass ISIA and ISTD - as the courses are all over the place at different times). BASI really is swings and roundabouts.
So, the other couple of options... Instructor Academy
, based in Soldeu in Andorra are a very good provided of CSIA courses. I've done individual courses with them (not their FastTrack course) and have always had top drawer course conductors and examiners (they can persuade the top guys to head over from Canada as it's a nice trip for them too). When I did my CSCF course, we had a World Cup coach who had been hired by BASI to redesign their coach programmes.
If your German is good you could also give the Austrian system a go... I've heard people have a great time doing the courses in Austria. I know of a Dutch company that run an extended programme, but am not sure of any English speaking companies that do...