What can I do with my degree in English Language and Linguistics?

Additional training may be required for a role in Speech and Language Therapy.  A solid grounding in linguistic analysis is essential in this field.

I want to work in Speech and Language Therapy

Speech technology, automatic translation, intelligent search engines, computer-mediated language learning and other areas hire linguists (e.g. Google employ linguists)

I want to work in Computing

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. History is a popular subject so it is important to build up teaching-related experience during your undergraduate degree and to apply each 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

I want to work in Teaching

This is a popular option and still relatively easy to get, although you would be wise to get the CELTA Certificate in TEFL as this will make the better jobs available - it can be done in one month. The JET scheme each year takes about 200 British graduates to Japan to teach English for one or more years and pays well - it is usually advertised in October each year with a closing date in November.

I want to work Teaching English as a Foreign Language

You may be interested in teaching and research in a Higher Education institution.   Alternatively, you might consider if progressing to PhD.

I want to work in a University

Additional training may be required for roles in Translation and Interpreting.

I want to work in Translating

Technical writing, editing, publishing and working for publishers specialising in language-teaching publications are all options for linguists.

I want to work in Publishing

You could consider roles as a forensic consultant or as a lawyer (with additional training).  This would use your verbal and analytical skills.

I want to work in Law

Many companies (e.g. The Gap) employ linguists to ensure that names of new products will have cross-linguistic appeal.

I want to work in Advertising

Many government agencies employ language and linguistics experts (e.g. MI5, Diplomatic Service)

I want to work in Government

Linguists can provide a better understanding of language use, pronunciation and practices; e.g. the BBC employs phoneticians who advise news presenters on how to pronounce foreign names.

I want to work in Consultancy

Linguists are employed as actor trainers (e.g. teaching specific accents or dialectal features), as consultants (e.g. to provide historical accuracy in language use) and as creators of new languages (like Dothraki in the Game of Thrones created by linguist David Peterson)

I want to work in the Film Industry

You may consider working as a linguistic consultant for dictionaries. 
Language documentation: document, analyse, and help preserve endangered languages by conducting fieldwork and establishing literacy programs

I want to work in Lexicography

Linguists are employed by law firms and many government agencies (incl. the police) are forensic consultants e.g. analysing speech and writing samples. See The case for forensic linguistics. There is an MSc in Forensic Linguistics at Aston University

I want to work in Forensics

Journalists research, write and present stories, features and articles across a range of media platforms – newspapers, magazines, television, radio and internet. Experience gained in student journalism will be helpful in breaking into this area.

I want to work in Journalism

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