It might be helpful to narrow down some industries that you might want to gain some work experience in- do you have any in mind? A great place to look into areas is by using the job profiles on our website- https://nationalcareers.service.gov.uk/
It might help to research the roles and focus in on the external links to have a look at companies or employers that may be related to the sector. This research might allow to to find employers, who you could contact and ask about work experience opportunities.
It could be beneficial for you to contact companies directly, to enable you to see whether there are companies which offer work experience opportunities in your area. To enable you to locate companies to contact you may want to look on the Yellow Pages website. This is useful as it may have names of companies you have not previously been aware of;
You can also webchat with our advisers, who might be able to offer you some further support on increasing your chances of finding work experience by using the following link-https://nationalcareers.service.gov.uk/webchat/chat/