What are local referendums used for?

Establishing directly elected mayors.
By 2016, 52 referendums had been held on moving to the directly elected mayor model, with only 16 approving the move.
The referendums were triggered by central government, a decision by the local authority or a petition by local citizens.
The proposal for an elected mayor was announced in November 2014 and Andy Burnham became the mayor in 2017.

Council tax increases.
A local referendum is needed to increase council tax by 3% or more in most areas.
Authorities responsible for social care are allowed to increase council tax by a further 2%.
A local authority proposing to increase council tax above a threshold set by central government must hold a referendum to approve it.
In 2015, voters in Bedfordshire rejected an increase proposed by the police and crime commissioner (PCC).

The Localism Act 2011 requires local authorities to hold referendums on neighbourhood plans for housing development.
By the end of 2015, 126 such referendums had been held and all of them approved the plans.
Turnout averaged 33%.
The Local Government Act 1972 allows voters to request that a parish council holds an advisory referendum on a local issue. The regulations were tightened after criticism that the system was being used to hold votes on issues that were not local matters (e.g. EU treaties).