UK universities can be categorised in a number of different ways. One of the earliest was by George Edwin Maclean in a 1917 report for the US Department of the Interior, who split the universities into ancient universities of England (including Durham), Scottish universities, the University of London, the "new or provincial universities", and the university colleges (Maclean's report only covered England and Scotland, Wales is thus omitted). The 1963 Robbins Report split the (then existing) universities into seven categories: the ancient universities of England, the ancient universities of Scotland, the University of London, the older civic universities of England (Maclean's "new or provincial" universities, with the addition of Durham, which at the time took in Newcastle), the University of Wales, the newer civic universities of England (mostly comprising Maclean's university colleges), and the new foundations in England (the plate glass universities). Divisions similar to these form the basis for groupings used commonly today.

Categorisation by age & location
In the early 1950s the University Grants Commission divided British universities by age into five groups by age and location. The English universities were divided into three: ancient, Durham and London, and the civic universities, with the other groups being the ancient Scottish universities (then the only universities in Scotland) and the University of Wales (then the only university in Wales). In modern usage, these groupings tend to be somewhat fuzzy in definition:

Ancient universities - the six universities founded before 1800, often subdivided into the Ancient Universities of Scotland and Oxbridge in England. When used historically it can also include the University of Dublin (now in the Republic of Ireland) and Marischal College, Aberdeen and King's College, Aberdeen (now merged to form the University of Aberdeen). The definition is sometimes stretched to include Durham and/or Dundee, both of which share some characteristics with the true ancient universities.
St David's College, Lampeter and Durham University - founded in the early 19th century as religiously-exclusive, residential university institutes, following the Oxbridge pattern. Neither fits well into the category of either civic universities or ancient universities.
University of London and its constituent colleges - founded in London from the early 19th century onwards as non-residential university colleges, following the pattern of the ancient universities of Scotland.
Greybrick universities - used occasionally, and in contrast to "Red Brick", to refer to the pre-Red Brick universities collectively.
Red Brick universities or Civic Universities - founded in provincial cities as non-residential university colleges in the later 19th and early 20th century, sometimes used to mean any university established between 1800 and 1992. As noted above, the Robbins Report included Durham as a Civic University, but since the separation of Durham and Newcastle it is more common to refer to Newcastle as a Civic University and to omit Durham from this group. Robbins divided the civic universities into two groups (older - the six red-bricks and Durham/Newcastle - and younger for later foundations), and also considered Keele to fall into this category..
Scottish Chartered Universities - Scottish universities created by Royal Charter in the 1960s covering three universities (Strathclyde, Heriot-Watt and Dundee) with origins as 18th and 19th century university colleges and one new institution (Stirling).
Plate Glass universities - new institutions created in the 1960s as residential universities with degree-awarding powers from the start (in contrast to being created as university colleges), formerly described as the 'new universities'. The UGC took the decision to create these universities in the late 1950s and early 1960s, prior to the Robbins Report, however the term is also frequently used to encompass the universities created as a result of that report.
Robbins expansion universities - Universities created as a result of the recommendations of the 1963 Robbins Report. This includes former Colleges of Advanced Technology (CATs), other former colleges, and the University of Stirling. These are often rolled in with the plate-glass universities and sharing their former description of 'new universities'. The term is sometimes erroneously used to describe the plate glass universities, which were already approved prior to the report.
The Open University - The UK's 'open to all' distance learning university (est. 1968).
Old universities - Institutions that were part of the University sector prior to 1992, including universities created by ancient usage, Act of Parliament, or Royal Charter, and full colleges of the federal Universities of London and Wales in 1992; this includes all of the above categories.
New Universities or Post-1992 universities - granted University status by an instrument of government under the Further and Higher Education Act 1992, including former Polytechnics, Colleges of Higher Education, and other Higher Education Corporations, but not including older university institutions that have gained University status since 1992 via royal charter (e.g., Imperial College or Cardiff University).

Mission groups
These are actual groupings with defined memberships:
Russell Group - self-selected association of 24 public research universities.
Million+ - coalition of post-1992 universities
University Alliance - coalition of "business engaged" (mostly) post-1992 universities.
Cathedrals Group - coalition of (mostly) new universities with historic links to one or more of the Christian churches.
Independent Universities Group - private universities.

Categorisation by structure
Unitary universities - the standard structure, with all teaching and services provided by the central University. Long standard in Scotland, the first unitary university in England was Birmingham in 1900.

Examining Board universities - modelled on the separation of teaching in College and examination by the Senate House in the University of Cambridge, the University of London (1836-1900) and the Royal University of Ireland (1880-1909) were set up to function purely as examining boards; there are no current universities in this category.
Federal universities - Starting with the Queen's University of Ireland (1850-1880) a number of universities have been federal in nature, including the Victoria University (1880-1904), the University of Wales (1893-2007), Durham University (1909-1963) and the Federal University of Surrey (2000-2004); the only current federal universities in the UK are the University of London (from 1900) and the University of the Highlands and Islands (from 2011).
Collegiate universities - the classical Oxbridge model of a university containing a number of colleges. In addition to Oxford and Cambridge, this has been adopted by Durham, York, and Lancaster, although these differ from the Oxbridge model in that there is no teaching in their colleges. The University of Roehampton and the University of the Arts London are also collegiate, with teaching taking place in academic departments associated with the colleges. Federal universities are also sometimes referred to as collegiate.

Statistical categorisation
A report in 2015 used grouping analysis to divide UK universities into four tiers based on how elite they were based on data on academic selectivity, research activity, teaching quality, socio-economic exclusivity and economic resources. The top tier consisted of only Oxford and Cambridge. The second tier contained the remaining universities from the Russell Group along with the former members of the defunct 1994 Group (except for the University of Essex), all of the pre-1992 universities in Scotland, and the University of Kent. The third tier was the remaining pre-1992 universities (with the exception of the University of Wales Trinity Saint David (UWTSD), which is technically pre-1992 as it operates under the University of Wales, Lampeter's 1828 Royal Charter), many of the former polytechnics and central institutions, and a few former HE colleges that became university colleges and then universities after the polytechnics. The fourth tier has the remaining polytechnics and the majority of the former HE colleges, along with UWTSD.