The UK has kept something close to a two party system in General elections. Labour and Conservative have alternated in power based on their ability or lack of it to improve living standards and preside over a successful economy. Labour’s bankrupting of the UK and trip to the IMF to borrow in the mid 1978s led to them being out of office for 18 years. The Conservatives adoption of the European Exchange Rate Mechanism and the predictable inflation and recession that caused led to Conservatives being out of office for 13 years. Labour’s boom and bust and banking crash of 2008 has so far led to them being out of office for 11 years.
I know some contributors here want a new or third party to emerge. The Social Democrats tried that in the 1980s and failed after a few by election successes. The Lib Dems are always positioning themselves as a potential new force but have never made it to first or second place in a General election and cannot truthfully claim to be new. The Referendum party, UKIP and the Brexit party tried it mainly around an important single issue but only ever won one seat in a General election between them. As I always advised here, if you wanted a referendum and then wanted Brexit done they had to be achieved with Conservative MP votes in the Commons. In Scotland the SNP has demonstrated that in the first past the post Westminster elections they have been able to break through into first place, displacing Labour, because they have made their constitutional issue more salient than economic management for the UK as whole.
On the continent there was the same alternation between Social Democrats and Christian Democrats in office in the last century. This century in all the main EU countries the big two have lost support with new populist parties emerging. It is true they have different voting systems which can assist splintering of the vote, but they had these same systems in the last century when Christian Democrats and Social Democrats were each likely to get around 40 % of the vote and to dominate coalitions with smaller parties formed by the winner.
This seems to have occurred because electors realise that unlike in the UK the once dominant parties can no longer guarantee or mess up the economy in the same way because they do not have the powers. EU control of interest rates, money and credit, state borrowing and some taxes changes things a lot. Elections are fought on other matters more.
The decline of the Christian Democrats has been speeded by EU policies. The lower tax greater freedom part of the conservative vote has been alienated by the compromises needed to accept a large and growing EU budget, independent collective EU borrowing, huge transfers at zero interest from surplus to deficit countries through the European Central Bank, and a regulatory colossus laying down detailed controls over many aspects of life. The conservative impulse has as a result been driven into newer parties of a more Eurosceptic tone. They are normally defeated by a coming together of all the other parties that are broadly pro EU to prevent any Eurosceptic movement gaining power again, as Syriza briefly did in Greece before its leaders gave in. In some cases as in France this has occurred in the second round of an election. In other cases as in current Italy it comes by excluding the Eurosceptic party from any post election coalition.