On my CV I've made it clear that my visa carries no employment restrictions and that I am eligible to work in the UK. If you apply for a job using an online application, they'll ask you those questions early on.
If you don't have much experience and are looking to beef up your CV, you could try volunteering. This will give you some UK experience and a UK reference which will definitely be assets in the job search. However, while volunteering is an excellent way to go, it's become really competitive in the recession or at least it has in Shropshire.
I went to one of my local charity shops recently (it had just opened) to pick up an application form and they had actually run out of them in less than 24 hours of being open. The woman had said they had a ton of people come in looking to volunteer. They also passed me over for the role because I didn't have UK references. So, that was a bit of a catch-22. I wanted to volunteer for many reasons including gaining a UK reference, but I couldn't volunteer because I didn't have a UK reference. One of my UK relatives is also having a lot of trouble finding even volunteer work. Your experience might be different though and it's definitely worth a shot.