Ah right the YMS... those days are a ways past now, I hadn't thought of that

When I first moved to the
UK - at 30 yrs old - I only had 1 yrs experience in software, but still found a job while living in
Ireland and subsequently got a normal work permit. I don't remember what was available for yoofs back in '02.
As you say going now, during an economic recovery/continued downturn, won't be easy. In fairness being outside or willing to go outside London, Brum, Manchester/Liverpool, might make it 'easier' to find a job. Certainly dealing with London, some folks seem allergic to go outside the M25. When I was hiring staff in '09 - with our office 30 miles from central London - I was disappointed in the quality of applicants, I expected a rash of superstars, but our recruiter said being where we were made in harder to find really good people, compared to London.
There are lots of great towns within 25-45 mins by train of central London (for when you want to get in on weekends or to catch a gig during the week) which have business parks, with lots of companies in them, nearby. The competition for jobs there might be less and therefore easier to find something. If you have a YMS then you can simply answer yes to the 'right to work' screening questions and hopefully find something

If you haven't already, I'd say to use indeed.co.uk to see whats available for your skillset near certain areas. It also doesn't hurt to just do some random surfing of multinationals you know are near where you want to live to see what they have on offer. Theoretically you've got the tough part - the visa - out of the way!
Oh, I am assuming a YMS means you don't need any subsequent proof of work eligibility for that 24 month period?