Media playback is unsupported on your device Media caption Jeremy Corbyn reacts to local election results after Labour suffers losses

Labour has suffered a net loss of council seats - starting from the low base of 2015 in many cases.

The Conservatives have lost more than 10 times as many councillors, but what is remarkable is that the main party of opposition - around the mid-term of a not-very-popular government - has not made net gains.

It seems reasonable to assume that some votes have been lost by Labour in Leave areas because - as the leader of Sunderland City Council Graeme Miller has said - the party hasn't decisively ruled out another referendum.

(It has retained it as an option, if the Conservatives are unwilling to change their deal).

But if you take a close look at the figures in Sunderland, the complexity of Labour's political problems are revealed.

Its vote fell by nearly 17 points there - while UKIP's went up by 4.5.

The pro-Remain Lib Dems saw their vote rise by nearly 10 points and the Greens by 8.5.

Indeed, the combined vote of the Lib Dems and Greens was 21.4%, not far off UKIP's 23.9%.

The swing from Labour to the Lib Dems was about 13% and to the Greens 10%.

Those in Labour's ranks who wanted a stronger commitment to another referendum on any Brexit deal are arguing now that the party is losing support in some Leave areas by failing to appeal enough to those who voted Remain.

Defections to the Lib Dems and the Greens suppressed the Labour vote, and further flatters UKIP's performance.

Local factors

In leave-supporting Derby, where Jeremy Corbyn's party lost six seats and UKIP gained two, the swing from Labour to Lib Dems was 6%.

But those who support Labour's current policy - a heavily caveated commitment to a referendum on Brexit under certain circumstances rather than a public vote in all circumstances - say this is too simplistic an analysis.

In truth, we can't discern the underlying motives of Labour/Lib Dem switchers in every part of the country unless we ask them.

There are genuinely local factors at play in some areas - unsurprising, perhaps, as these are indeed local elections.

And some on Labour's left have another theory. They say the party is vulnerable to a protest vote because some Labour councils have had to cut services due to constrained budgets.

In some cases the Lib Dems are the beneficiaries

Others on the left say the party can't get a hearing for its anti-austerity message as the Brexit debate muffles all else.

They are actually quite keen for their party leadership to reach a deal with the government soon to get Brexit over the line and - they believe - this will then neutralise the political toxicity of the issue.

But there is little doubt politicians will proclaim to know the will of the people, without necessarily exploring deeper motivations - and the results will be interpreted in a way which advances their own arguments.