Heya, have you checked your local council's website? There might be a "Jobs" section where they post all the available roles up, I know that's the case with my County Council. If you can't find it, then search for 'jobs' in the website's search bar or click on "Get Involved" or "About the Council" etc.
It is really hard to get a job in Post Office these days, you can check for jobs in Royal Mail website all day long. But it is incredibly hard to get, my dad has experienced this for years. You can probably very easily get in if you have any mates working there. In terms of Council than go check the website and you might also want to ask the receptionist in the council as well for any job vacancies.
theyre recruiting for more temp staff during the olympics for north london, and probably will be vacancys for saturday staff. but i doubt there will be anything better than that for a while, at the moment all the offices are getting restructured; the rounds are getting bigger so anyone who hasnt been in the job for that long i.e. less than 2 years face having their contract not renewed