In many respects it seems obvious to conclude ‘yes’ to this question, that the UK is a liberal democracy. The UK enjoys free and fair elections, experiences smooth transitions of power from one government to the next, and is generally a tolerant society whose politics has been opened up by the Freedom of Information Act.
However, there are some major criticisms which we can level, and these stem from the fact that the UK constitution does not successfully limit governmental power, nor does it entrench our human rights. On the latter point, any British government could in theory alter our key human rights by simply passing a Bill through Parliament. In most liberal democracies, it would require a lengthy challenge to a constitution, making it harder to make any such changes to citizens’ rights.
With regards to the UK’s failure to limit government power, a good example (see video link below) is the decision by the Labour Government to go to war with Iraq in 2003. As evidence to the Chilcot Inquiry indicates, Tony Blair made this decision himself, largely side-lining Cabinet and Parliament in the process. This particular issue demonstrates that in the right circumstances, the UK Prime Minister is very powerful.
Any assessment of the success or otherwise of liberal democracy in Britain cannot ignore this point, and in any essay you write making such an assessment will require you to tackle this issue.

The summer holidays will soon be upon us, and no doubt both students and teachers need a break. But so too does our prime minister – apparently. Labour MP Austin Mitchell, has described Brown as “knackered”, and runs the risk of making bad decisions unless he takes a break. Still, that’s nothing. Another Labour MP, Patricia Hewitt has criticised the “laddish” culture at Number 10, and hence Gordon Brown’s running of it. Oh dear, with friends like these who needs enemies?