Google, and most other search engines, provide parameters which you can specify to tune your searches, to enable you to find the information you're looking for.
One such parameter is site:
the site: parameter will cause Google to only return results which relate to the domain you're interested in... including all subdomains!
so if you're looking for a Network Manager job in Cheshire, for example, googling: site:cheshire.sch.uk "Network Manager", will return all Network Manager references on any Cheshire school sites; which is usually only when the job is available.
Note: the quotes around the job title also indicate to Google that you are only interested in results which contain that exact phrase, as apposed to Network or Manager.
Another useful tweak, is filtering the results to the past month, to only find recent and likely still available vacancies. This can be achieved, either through the Google options side panel, or by appending &tbs=qdr:m to the search url.
Also: Adding extra keywords such as vacancy may filter out any unwanted results, however it may also reduce the number of results which are of interest, if they don't contain the word vacancy.
Give it a try, I hope your job hunting goes well.