Just as the Greens caused a sensation in the European Parliament elections 15 years ago by finishing a strong third behind Labour and the Conservatives, so the United Kingdom Independence Party looks set to cause a similar sensation in a fortnight's time.

The only difference is that, whereas the Greens in 1989 failed to win any seats in the Strasbourg Parliament under the old first-past-the-post electoral system, UKIP under proportional representation now could easily gain a dozen seats or more.

Success on that scale would propel UKIP into the centre of national political debate. It would also dent the Conservatives' European prospects because UKIP takes its support disproportionately from among people who are normally Tory supporters.

That said, YouGov's survey for The Telegraph suggests that UKIP's appeal is almost entirely focused on Europe. There are no signs of UKIP making a major breakthrough at the local or national levels. There are also no signs of the British National Party making major advances on any level, though it will probably pick up a scattering of council seats in its strong areas.

YouGov estimates that the percentage turnout in the local and Euro elections this year will be in the mid 30s, conceivably in the high 30s. When seats in the European Parliament were last contested in 1999, turnout in Britain - 24 per cent - was the lowest anywhere in the EU.

However, the Government's decision to hold this year's Euro elections and the annual round of local elections on the same day will almost certainly raise turnout to more normal local-election levels. The holding of all-postal ballot elections in four English regions should also raise the number of people casting their votes.

YouGov asked respondents across the country how they would vote - if they voted - in the Euro elections, in any local elections held in their area on June 10, and at a UK general election if one were held soon.

The results, set out in the section of the chart headed "Voting intentions", show that large numbers of voters clearly differentiate between the three types of election and also that the level of turnout in the Euro elections will be crucial.

Among all eligible electors, the Conservatives and Labour are neck and neck in the Euro elections, with the Liberal Democrats a comfortable third and UKIP fourth. However, among the 39 per cent of YouGov's sample who say they are "very likely" to vote in the Euro elections next month, the picture changes drastically.

The Conservatives, whose supporters are most likely to turn out, forge ahead. Labour, whose voters are least likely to turn out under present circumstances, falls back. The Liberal Democrats also lose support and UKIP moves up from fourth place to third.

On that basis, the Conservatives would "win" the election while actually, under PR, winning less than a third of the seats - a lower proportion than they hold now. Labour would lose the election on any basis, winning less than a fifth of the seats - also a lower proportion than it holds now. The Liberal Democrats would win roughly one seat in seven - yet again a smaller proportion than they hold now.

The real winners, in the sense of the party making the largest gains (possibly the only gains), would be UKIP. Among the 87-strong British delegation to the European Parliament, UKIP currently holds only three seats. Even though Britain's delegation to Strasbourg has been reduced from 87 to 78, it looks as though when the ballots are counted on June 13 it could find itself with between eight and a dozen seats, possibly more. Most of this UKIP vote is undoubtedly a "protest" vote but one that is not nearly as diffuse as past protest votes have usually been.

The UKIP protest is targeted specifically at the EU, the Brussels bureaucracy and Europe's increasing interference in what UKIP supporters see as Britain's internal affairs. YouGov's findings show clearly that a majority of people in Britain are not desperately interested in Europe and do not know a great deal about the European Union but are adamant - at least for the time being - that so far as the UK is concerned the great European project should be, if not reversed, then at least halted in its tracks.

Those who intend to vote UKIP next month feel more strongly about these matters than most Britons and would go further than most in distancing this country from the EU. Nevertheless, there can be no doubt that the views of UKIP supporters on Europe broadly represent majority opinion in this country.

The figures in the chart reveal both people's lack of interest in Europe and their ignorance of it but also most Britons' generalised antipathy towards many of its current manifestations.

As the figures show, only 13 per cent of YouGov's respondents are "very interested" in the European Parliament elections, a mere three per cent feel they know "a great deal" about the Parliament's powers and responsibilities, and a majority confess that, if they bother to vote at all in the elections on June 10, they will vote mainly not to influence the composition of the European Parliament but to express their views about the political scene in Britain.

As regards their knowledge of broader European affairs, a large majority of Britons are in a state of ignorance that may or may not be blissful but is apparently unembarrassed. Fully 58 per cent of YouGov's respondents admit they have no idea who presides over the European Commission, only 23 per cent can correctly name Romano Prodi, and the rest guess wrong (including five per cent for Italy's prime minister, Silvio Berlusconi, and three per cent for the French president, Jacques Chirac).

Even though the last European Parliament elections were also held under PR, only 31 per cent of YouGov's respondents realise that if they vote on June 10 they will be voting for a regional party list rather than their local MEP. Among those most likely to vote, the proportion rises to just 41 per cent.

As for a proposed new European constitution, only 21 per cent say they would vote in favour of such a constitution if a referendum were held now and two thirds of British voters - as the figures in the chart make plain - are opposed to Britain's surrendering its veto in fields such as defence, social security, taxation and the courts and criminal justice. The Government's "red lines", in most voters' view, must not be crossed.

This year's local elections will almost certainly mark a contrast with the Euros, with the local results conforming to a more familiar pattern.

YouGov's findings suggest that the Conservatives will come in ahead of Labour, making substantial gains in both seats and councils, and that the Liberal Democrats - always strongest in local elections - will more or less hold their own.

Interest and a sense of involvement in the local elections are at a considerably higher level than in the Euros.

Whereas only 27 per cent of voters reckon they know "a great deal" or "a fair amount" about the European Parliament's powers and responsibilities, double that proportion, 54 per cent, claim the same levels of knowledge about the powers and responsibilities of their local council.

An even larger number, 60 per cent, think those powers and responsibilities are substantial.

Similarly, whereas only 28 per cent of YouGov's respondents say that, if they vote in the Euro elections they will be voting "mainly to influence the composition of the European Parliament", the proportion among those saying that, if they vote locally, they will vote "mainly to influence the way their local council is run" rises to 54 per cent.

Predictably, sharp rises in council tax top the list of issues that people say will determine how they vote, if they vote, in local elections on June 10.

The low quality of local services and the failures of the Blair Government are some way behind.

YouGov elicited the views of 1,928 adults across Great Britain online on May 20 and 21. The data have been weighted to conform to the demographic profile of British adults as a whole.

Anthony King is professor of government at Essex University