As others have said, she cannot simply apply for a SIN. It doesn't work that way.
The IEC / Working Holiday Visa program is her only 'easy' option to be able to work here. But as others have explained, there are limited spots available for the UK because a lot of people who want a spot. She should submit her profile as soon as possible and hope she is selected (there is absolutely no guarantee she will be selected). You can find details here:
http://www.cic.gc.ca/english/work/iec/eligibility.asp
Otherwise it will be very difficult for her to be able to work in Canada. She would either need to apply to immigrate (to become a permanent resident). This is a long and expensive process - and it's quite possible she may not qualify if she doesn't have the right education and work experience. The other option would be to find an employer who is willing to give her a full time job and also obtain an approved LMIA so that she can apply for a work permit. It's generally next to impossible to find employers who are willing to go through the LMIA process.