If you’ve already completed a degree at an institution in the UK or in another majority English speaking country, then you may be exempt from an additional English language test if this has been within 2 years of the start date of the programme you are applying to.
The Business School, the School of Government and International Affairs, the Computer Science department and the Psychology department all require the full degree to have been taught in a majority English speaking country, whereas other departments may consider if only part of the degree has been (eg the final year of a 3-year undergraduate degree).