Comically large swings to the Liberal Democrats in the commuter belt marked a night in which, in keeping with the fragmented landscape of British politics, there is not a single message from the electorate, but several. Despite the threats, the Conservative section of the electorate didn’t go on strike over their party’s failure to deliver Brexit. Turnout was generally down a bit, but recent political turmoil has not resulted in a big drop in participation, as had been feared.

In councils where major party organisation is strong, such as Southampton and Bury, it was only down 1-3 percentage points on last year. While this is not encouraging, neither is it a reversion to the very low turnouts that prevailed in the tranquil sets of local elections in the 1997-2003 period. In some individual areas, turnout was actually pretty high – in Sunderland it seemed to help Ukip, while in the London commuter belt it helped the Lib Dems.

Labour performed poorly and the Conservatives did surprisingly well in many areas where there are marginal councils and parliamentary constituencies. Labour failed to make what should have been easy gains in Dudley, Swindon and North Warwickshire. Labour generally did worse than in 2018, and almost everywhere worse than in 2016, in councils where direct comparison is possible. There was a seven-point swing to Conservative since 2018 in Dudley, and a two-point swing in Southampton. This slippage is masked by the fact that the Conservatives were defending seats won at their recent high tide of 2015.

Not only was Labour dented in the marginals, but the party also suffered in what should be safe territory. Losses to Ukip and independents in heartlands such as Sunderland and Bolsover are ominous, as is the ability of the Conservatives to make collateral gains in such areas. Labour also went into reverse in some of its more metropolitan and liberal strongholds, with Lib Dems, Greens and Independents making progress in suburbs such as Wirral and university cities such as Exeter.

Although the Tory defences held against Labour, they were blown away by the Lib Dems and localist parties in places that had recently been regarded as safe. The swings to the Lib Dems across the commuter belt, often topping 20% since 2015, caused seats to tumble in places such as Wokingham, St Albans and Chelmsford – where the Lib Dems made 26 gains from the Tories and took control of a council where they had previously only had a group of five councillors. Labour’s contribution to Tory defeats was marginal at best, but in places such as Hart (Hampshire) Lib Dems and Resident parties marched arm-in-arm. While Brexiters refrained from giving the Conservatives a kicking, remainers had no compunction about administering some stinging defeats. The installation of a Lib Dem council in Jacob Rees-Mogg’s constituency in Bath & North East Somerset will be particularly piquant.

Some of the pattern of the swing may reflect those “local peculiarities” that make local elections so interesting. While each council is its own political environment, there are some common features. Labour has run most of the metropolitan borough councils for a very long time. Councils by their nature tend to do unpopular things, and local grievances will accumulate. The period since 2010 has been particularly tough for councils because of the harsh spending cuts that they have suffered from central government – “outsourcing austerity”, as councillors describe it. There have been a lot of painful cuts, and a slow deterioration in the public realm. Labour’s traditional voters notice and give their councils a share of the blame.

It is significant that Labour’s best metropolitan result came in Trafford, where the party had only run the borough since the 2018 elections, having ejected a long-serving Conservative council. Locally, Labour still had the benefit of being the party of change.

Similarly on the Conservative side, Tory councils get stale and unpopular, and unlike Labour councils cannot blame central government for austerity. Particularly in the south-east, they are also under pressure to build housing, which stimulates environmental and nimby objections that Resident parties – and Lib Dems – can easily convert into political opposition.

We like to read the broad pattern of local election results in terms of the ebb and flow of support for the national parties, but there is a lot more going on under the surface. As well as Brexit, the impacts of austerity and the housing shortage are there to be seen in the results.

• Lewis Baston is a political analyst and writer