What can I do with my degree in Classics and Archaeology?

Archaeologists are employed in national agencies, local authorities, museums, universities, planning consultancies, and private practice, undertaking a wide variety of activities from field practice to laboratory work, information management to education, specialist research to artefact curation and display.
Job profile of an archaeologist from the Prospects website
Job profile of an archaeologist from the TARGET Jobs website

Archivists work in national and local records offices, specialist organisations (such as Canterbury Cathedral) and in businesses. They acquire, manage and maintain documents and other materials that have historical importance and make them accessible to researchers and other users.
Job profile of an archivist from the Prospects website
Job profile of an archivist from the TARGET Jobs website
The Archives and Records Association
I Want to Work In: Librarianship and Archives

Acquires, cares for, develops, displays and interprets objects and collections of historic interest. In small museums, the curator is also responsible for managing the collection, operations, staff and volunteers.
Job profile of a museum curator from the Prospects website
Job profile of a museum exhibition officer from the TARGET Jobs website
The Museums Association
I Want to Work In: The Heritage Sector

To teach in state schools (excluding academies and free schools) in England and Wales, you must complete a period of “initial teacher training”, such as a one-year Postgraduate Certificate in Education (PGCE) course or school-centred training, which leads to Qualified Teacher Status. It is important to build up teaching-related experience during your undergraduate degree and to apply early for teacher training.
Job profile of a secondary school teacher from the Prospects website
Job profile of a secondary school teacher from the TARGET Jobs website
Get Into Teaching website from the Department for Education - explains the various routes into teaching

I Want to Work In: Teaching

As well as teaching through lectures and seminars, academic staff in higher education also carry out research and a wide range of administrative and pastoral tasks. Although a teaching qualification is not required, you will need a higher degree, normally a PhD. Competition is strong for entry-level academic posts.
Job profile of a higher education lecturer from the Prospects website
Job profile of a higher education lecturer from the TARGET Jobs website
I Want to Work in: A University