I know it might seem a bit of a faff, but it might help you to have several versions of your cv, depending on what type of job you're applying for or even the exact job. As an example, in my 20s I applied for administrative/secretarial, information type roles, and customer services, and I had 3 different cvs, highlighting the skills for that particular job type. I also found it essential I used the covering letter to make sure I listed my how I met the essential criteria and sometimes the desirable criteria in the job description. Many places simply don't have the resources to train anyone any more, so they expect you to come in "shelf ready" as it were.
Years ago I also had some very good advice from a careers adviser - put your name at the top of the cv, not curriculum vitae, and underneath a contact email address and telephone number. Don't include your home address, or marital status, or date of birth, or any of that stuff which used to be so popular. Then put a short summary underneath, e.g. "Skilled, experienced, enthusiastic and hard-working cucumber picker with over 10 years' experience seeks new career opportunity in the industry." (Thanks to previous poster who gave good advice.) Then include a skills profile, before going on to give your employment experience, starting with the most recent; then your education and qualifications - don't give the year unless it's within the last 5, which is apparently the "shelf life" of most qualifications without updates. At the end of the cv put other information - clean current driving licence, for instance; and at the very end under references you could put "available on request".
You don't say what sort of age you are or the type of work you're looking for (is it very competitive? like you, I'd have thought there should be jobs in London!) or where you're looking for vacancies - all of these might change the advice slightly. If it's an application form you need to complete then the "additional information" section, where you tell them how you're the best person for the job, is the absolute key. Also, remember that often a first sift will be done by a busy HR department or stressed out line manager, and they'll usually have a tickbox sheet, so the easier you can make their life the better.