Rules and regulations
Anyone can run a dating site - it would be quite possible to start one up tomorrow. You don't need a licence, you aren't obliged to meet or vet your clients, and once you have set up your agency there are no statutory checks on how it is run – although many of the biggest names in the dating sphere, such as match.com, are starting to run background checks on new members as a goodwill gesture for existing users
There is a trade association, the Association of British Introduction Agencies (ABIA), which you could join but it isn't compulsory. Having said that, you can get support and advice from the association and membership will give your clients confidence.
To be a member of the ABIA you need to adhere to a strict code of practice, which you can then show to any prospective clients before entering into an arrangement. The code details what is expected of both client and agency (in terms of data handling, advertising and complaints) so everyone is fully informed at the start.