I have failed my MSc, by which I mean, I will not be able to proceed but could be awarded a posgraduate certificate for the modules I have already passed. To be fair I must say I already hold an MA, but all the same, I am considering re-applying somewhere else for the MSc in the same subject but maybe on a distance learning course. However, when I raised this point with the course director she was livid and told me it wasn't possible to do that. Is this true?
I thought this was up to admissions to decide.

There's nothing stopping you reapplying, and you are correct in saying it's up to the admissions department to decide whether to let you do the MSc.

I think it is frowned upon though so certain universities might not like it and won't let you do another MSc. Of course, you could always omit the fact that you ever attended an MSc course and just put on your CV that you have a PG certificate. Depends on your integrity I guess.

It's an educational marketplace out there so if you are willing to pay the money and they are willing to take you so be it. I suppose the question is why the MSc? is it MScRes? The open University do an Mres, they are also more fexible on entry requirements. Good luck :-)

If you've failed because of academic dishonesty, don't try and transfer the credits or resubmit the failed work elsewhere - they will want a reference from your current university and the referee will be obliged to explain why you were thrown out or turnitin will find you out. I suspect this is why the tutor was livid.
If you failed because your work was poor, I'd ask why you think it would be easier through distance learning, where you have limited contact to tutors? If anything, that's the harder route. Perhaps it would be better to accept that whatever this course is, it's not your strength and find another path?

How did you fail?

Bewildered is right. I did a PGCert as I couldn't progress and it is tough going with the MSc with distance learning and sometimes that can be an issue. I got my MSc with the OU and Liverpool University mentioned that I didn't do labs even though my PGCert is via a red brick uni.

Just my 2 pennies.

The other posters are right - the key issue is to know why you didn't pass. Maybe now is a really good time to (a) get as much feedback as possible from your tutors on your work, and (b) ask their honest advice on career directions or educational choices you might take.