The trouble with agencies is that the good ones are good, the bad ones - not good. When I was searching I found some adverts fake, some were real vacancies that had been filled but the agency left them up to boost the numbers on the site. I once saw an advert for a company that was just being wound up - they had just made me redundant.
Look at the adverts and see if they appear on several agencies. The wording usually stays the same so it is easy to see if the job is legit. However most jobs in the UK are not advertised - they are filled by word of mouth or by an HR department having flagged a CV they have received.
I would recommend just putting some contact details on your CV, no exact address, no exact date of birth. This will reduce the chance of anyone being able to clone your identity.
Above all, include a covering letter that highlights your strengths and your compatibility with the job in question. This should be tailored for each application.
Good luck
Neil