In what circumstances are referendums held in the UK?

Referendums are sometimes held because a party cannot decide on an issue; a referendum is held to stop a party splitting. Due to the heterogeneous make up of the major political parties, certain issues divide those at opposite ends of the inter party spectrum. Take the conservative party, for example. It could be argued that, to an extent, one of the reasons they have promised a referendum on the EU is to keep the far right Eurosceptics (37 MP’s prepared to vote against their party on membership of the EU) happy. An example of a referendum that happened specifically because of an inability of a government to come to a decision is the AV voting referendum 2011. This took place under the coalition government, comprised of the Conservatives and the Liberal Democrats. The Lib Dems wanted to reform the voting system whereas the Conservative, a party that does well under first past the post, wanted it to stay as it was. The voting system did not change.
In addition, referendums are held in circumstances when an important change with a lasting legacy needs to be made. This is called entrenchment. By having a referendum, it makes it ever the more difficult for future governments to reverse the decision made, as it now has widespread public knowledge and support. A referendum does then, in effect, secure permanence. An example of a referendum that took place to entrench reform posed the question ‘Should there be a Scottish Parliament?’. This was a Labour party manifesto agreement and the result was that there should be a separate parliament.
Furthermore, a referendum may be held when the government needs to secure public consent on an issue. This maybe because the decision being made is somewhat controversial or because the success of a policy is dependant on the backing of the public. An example of the latter is the Approval for the Good Friday Agreement. This referendum took place to materialise an agreement that had been previously decided. It occurred to signal an end to the the long peace process in Northern Ireland. As said by the IRA themselves the Agreement needed to be able to ‘deliver a just and durable peace in our country’, showing how important public support of the referendum was. The agreement was approved by a 71% majority.