Origins of great great great grandfather's work in a legal firm.?

I have never heard the name of your ancestor's firm. It would have become a solicitors practise in around the 1870s when the Law Society was formed. Attorneys became an obsolete term in the UK, lawyers being known either as 'solicitors' or 'barristers'. I can say your ancestor was the former as barristers have never formed firms. Incidentally, I think the last name would have been D'Eath, which is the usual spelling . As to how to trace them. Try writing to the Law Society, Chancery Lane, London WC1. I'm not sure, however, how far back their records go. If they cannot help, you need to go through old trade directories for Clement's Inn. That would show you how long the firm remained at the address, but not where they moved to - if that was the case. Buildings called that still stood when I was a young man in the 1960s as I used to visit an address there regularly.