The first thing you should do when looking for a new job is visit the jobcentre plus office to ensure you get the benefits you need but also to check their database of Liverpool jobs and Merseyside generally on a regular basis. You can also do this online at the official government jobcentre plus site. See here for a list of Liverpool jobcentre plus offices
Secondly you should register with all the local Liverpool job agencies and either email them an updated version of your CV or take one with you when you go to register with them.
You should also upload your CV to the major job search engines like Monster.com and Reeds as well as searching their sites for the latest job vacancies in Liverpool.
Other websites you should check out for the latest Liverpool jobs are fish4jobs and gumtree
Many of the major companies today also show the latest vacancies on their own websites so you should always check with them and if they are showing current vacancies then you can apply for them there and then on their own website.
You should also send out letters and CV's to companies you would like to work for even if they are not advertising. You could get lucky and the fact you are doing so shows that you are motivated, empowering yourself and taking control of the situation. Employers like to see this quality and even if they have no current vacancies they may place on file until one comes along. Also try calling companies on the off chance too.
Dont forget to check the Liverpool Echo, Daily post and even the national papers too, the Daily Mirror and the Daily Mail often advertise lots of job opportunities on Thursdays.
If you follow all these methods then you will significantly improve your chances of landing a job sooner rather than later. Good luck with your jobsearch .