Newspapers
National newspapers and local newspapers all have job adverts. The Guardian and The Times are popular national newspapers with different industries grouped on different days. For example, Education jobs are in The Guardian on Tuesdays. Both newspapers also have job websites:
The Guardian
The Times
Specialist Industry Publications and Websites
Keep up with industry news and find the specialist jobs this way, such as AdWeek for advertising vacancies or TES for teaching jobs.
Job Centre Plus
Job Centre Plus is part of the government's Department for Work and Pensions. Companies can list vacancies for free and jobs are on their website and at Job Centre offices across the country. In the offices you can search their database for jobs and print the details for free. Advisors are there to help you complete application forms too. But it can be busy and it's where every unemployed person receiving government unemployment benefit must register every two weeks so it can be very busy and jobs go quickly.
Employment Agencies
There are lots to choose from so source an agency that deals with your kind of work. Look at ads in specialist magazines and on industry websites and see which agencies are advertising there. Then, contact them and get an appointment to register. Treat it as a job interview because if they like you they'll work harder for you. It is against the law to be charged a registration fee or a job finder fee as employers pay the agency for finding the right person.
Websites
As you would expect, there are plenty of job websites in the UK but the largest seem to be Monster and Total Jobs.
Obviously the vacancies here gets hundreds, if not thousands, of applications a day so it a very competitive world. It may be better to source your industry's most popular websites and check there for jobs.