Is it acceptable to telephone supermarkets and ask if they have any job vacancies?
Or should you only enquire about jobs if they are advertised in store, with the Job Centre etc?
I would go to the store, ask someone stacking shelves who to speak to about a job, they will give you the manager’s name. Find the manager. "Mr Smith, I wonder if you can help me? I like Sainsburys and would very much like to work here, when do you think you might have a vacancy?"
not "do you have a vacancy?" because the answer is yes or no.
asking nicely if someone can help is a great way to start, nobody can say "no"
No Vacancy

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Where can I find details of vacancies working for Jobcentre Plus?
When I search for Jobcentre online it brings up details of jobs they are currently advertising, rather than vacancies actually working with them.
It’s now found at www.direct.gov.uk/jobs
Hope this helps.
Good luck with your job hunting.
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No Vacancy
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Lieutenant Cade Grant is rugged and gorgeous, but his heart is as hard as they come.Innocent Liv needs work fast; if she has to be housekeeper to the brooding lieutenant then so be it!Soon Cade wants his virginal maid between his sheets, not washing them. The job vacancy s now in his bed–and Cade ll teach her all she needs to know….