Both main national parties in Parliament lost votes and seats in the Council elections. The failure to get through Brexit as promised annoyed a lot of voters who wished to vote for anyone other than the two main parties as a result. The Conservatives were blamed for promising an exit with or without an Agreement by 29 March 2019 and then delaying. Leave voters were annoyed we are not out, and firm Remainers worried that nonetheless the party still says it wants to leave. Labour were punished for changing their Manifesto position of 2017 with a view to watering down or delaying Brexit by Leave voters, and by Remain voters for not being clearly in favour of revocation or a second referendum.
The Council elections were not a second referendum on Brexit, as the Brexit party did not stand, and as the switchers away from Labour and Conservative were both Leave and Remain supporters. There was a mood to vote for anyone who was not a candidate for Labour or the Conservatives in quite a few cases. Independents did well, without expressing a particular viewpoint on the EU referendum.
There were various local issues Council by Council, where some incumbent Councils were unpopular for perceived failings on their local decisions. Many of the doorstep conversations I had in the Wokingham and West Berkshire contests were about local issues.