Well, if you are Letting Agent then you need to do so in order to comply with the Data Protection Act
The Data Protection Act requires that Letting Agents do not share any information that they obtain from someone in one circumstance, with someone else without the person knowing about this and agreeing to it prior to the exchange of information.
Landlords are not required by law to do so, however it is still good practice and will probably work out better for you.
Because you will be warning the tenant that if they do decide to ruin your property, or leave with thousands of pounds of unpaid rental arrears - they will have to live with having their details stored on BadTenants.co.uk. Which is easily searchable by landlords and letting agents up and down the country.
Insodoing, potential bad-tenants may be put off from trying to cheat you out of money. Or if they do then they won't wonder why no Landlords in the UK will let them into their properties.