I don't know what grades you've got but, if you haven't got high enough grades to get in one of the universities that was a university before 1992, the following are best regarded for game design, from best to least:
For context, University College London (1st in Europe, 4th in the world, for this subject), then Nottingham, then Imperial College London, are at this level.
Nottingham Trent (origin 1843). 4th best in the UK for this subject. 17th in Europe, 58th in the world.
For context, Manchester, then Kings College London, then Glasgow, then Queen Mary University of London, then Oxford, then Ulster, are at this level for this subject.
Essex (has always been a university - since 1965 - and tends to have more achievable grades than most other universities of its generation).
Sussex (has always been a university - since 1959 - and tends to have more achievable grades than some other universities of its generation).
University of the West of England, Bristol (origin 1595, but you wouldn't know it to look at it. Looks like a university of 1990s origin)
For context, Edinburgh is at this level for this subject.
Bournemouth University (origin early 1900s)
For context, Cambridge is at this level for this subject.
Coventry University (origin 1843)
Plymouth University (origin 1862)
Liverpool John Moores (origin 1823)
Brunel University London (has always been a university (since 1966) but might have more achievable entry grades than some other London universities)
Reading University (has always been a university (since 1892)- it was once classed as a constituent college of Oxford University) and tends to have more achievable grades than even some lower ranked universities for a particular subject than it.
University of East Anglia - always a university (since 1963) and may have more achievable grades than some other universities of its generation.
University of the West of Scotland (origin 1897)
Heriot-Watt (in Edinburgh) Origin 1821.
Portsmouth. Origin 1870.
Salford. Origin 1850.
Manchester Metropolitan. Origin 1824.
Bangor - always a university (since 1885) and has more achievable grades than many universities of its generation.
For context, Durham University is at this level for this subject.
Teesside. Origin 1930. Degrees were originally validated by the University of London.
For context, Exeter is at this level for this subject.
Leicester. Always a university (since 1921). It once had its degrees awarded by the University of London. It tends to have more achievable grades than even some lower ranked universities for a particular subject than it.
East London. Origin 1898.
City, University of London. Origin 1852. University since 1966 with more achievable grades than some other universities of its generation.
For context, St Andrews is at this level for this subject.
Hertfordshire. Origin 1948. 54th out of 76 in the UK, 207th in Europe, 469th in the world, for this subject.
For context, Dundee, origin 1897 as a constituent college of St Andrews, university since 1967, is at this level for this subject.
Source: edurank.org
To work out if you are considering the best available places to you for your grades and requirements:
What are your predicted grades?
Which areas of the UK and Ireland would you consider studying in?