How likely is it that I will find a desperate company hiring for business admin

Within a week? Practically zero.

It's because I have a phone appointment with the job centre on Friday but I can tell them I had an online interview recently (not a desperate company and I won't tell them anything about desperate companies), I did all of the talking in that online interview and it was good for a first interview that I haven't had in ages. There is also some travelling involved like going to the city so it would be good if I don't get it, but the point is, I can tell job centre I have had an interview since my last job so they can't sanction me.

If you’ve had an interview you can tell them you’ve been interviewed, yes.

I was just wondering whether I could switch employers, as in I applied for an apprenticeship with the same training provider and different employer. I am sure the training provider still has my details, would I be able to speak with them and switch employers or do I need to start from the beginning and go for the interview?