Britons are not all alone in their scepticism about Europe. If it should really come to a British exit - Brexit - from the European Union, the effects would be felt in many EU member states.
This is a fear being openly discussed in Brussels, for example in recent remarks by European Commission head Jean-Claude Juncker. He is concerned that a Brexit could trigger a "desire for more" elsewhere.
What follows is a survey of possible national referendums in member states concerning membership and other EU-related issues:
HUNGARY: Plans by the conservative government of Premier Viktor Orban for a referendum over EU refugee quotas are far along. The issue would concern future refugees, not those quotas already agreed on. Budapest is already challenging the latter before the European Court of Justice. A referendum is foreseen for the autumn, though an exact date has yet to be set. First the Hungarian constitutional court is studying whether the referendum issue is in keeping with the constitution while not violating international agreements. The opposition in Budapest said it will boycott the referendum. For a referendum to be valid, a turnout of at least 50 per cent of eligible voters is required.
CZECH REPUBLIC: The upcoming vote in Britain has triggered a "Czexit" debate, with Social Democratic Premier Bohuslav Sobotka warning that a "wave of nationalism and separatism" throughout Europe could result if Britain quits the EU. Observers fear that the issue could dominate the Czech parliamentary election campaign in 2017. In early May, a motion by the right-wing Usvit (Dawn) party seeking debate over an EU exit referendum was turned down by the Chamber of Deputies, the lower house of parliament.
POLAND: No referendum initiatives are currently being planned by the government. The nationalist movement - part of the Kukiz15 party in parliament - has begun a campaign for a referendum on whether the country should take in refugees or not. Recent surveys in Poland show 70 per cent of respondents opposed to letting refugees settle in the country.
NETHERLANDS: Opinion surveys show a majority of the Dutch favouring a referendum on EU membership, but current laws allow only for an "advisory" referendum as an instrument of popular will. This was exercised in April, when under an initiative of eurosceptic civil groups rejected the EU's association treaty with the Ukraine.
FRANCE: Marine Le Pen, head of the extreme right-wing National Front, regularly renews her demand for a referendum on France quitting the EU. A referendum is only possible in France if the president agrees. Bruno Le Maire, a potential candidate for the centre-right Les Republicains party in the 2017 presidential election, is also calling for a referendum, but his takes aim at EU treaties in a bid to strengthen the EU.
THE BALTICS: There is more enthusiasm for the EU to be found in Estonia, Latvia and Lithuania than in many of the older western member states. But various crises have given a boost to right-wing populists and those people sceptical about the EU. Individual opposition parties and anti-immigrant forces have been demanding referendums over refugees and immigrants. The governments in Tallinn, Riga and Vilnius have so far not bowed to such calls.