Some good analysis above.
It's a good day for Labour, but in all honesty, thats what you expect in local elections from whomever isn't in government and in that context it's not as good as Labour would have historically expected. Also, more evidence that the party are becoming increasingly popular in wealthier, metropolitan cities and parts of London and are still struggling to enthuse more traditionally working class communities in the north. Nothing we didn't know before.
Still lots to count, but Tories will probably be okay with it. They expected a kicking, they got a kicking and sometimes people want to punish parties, and having done so are sometimes more open to voting for them again.
Lib Dems have done well. They often do at local elections. Might be the start of a return to prominence for them after brexit etc. Lots of southern Tories will be more content voting for Lib Dems than Labour.
Greens picked up a few, no bad thing. Interesting from a Labour perspective though who probably want to keep that genie in the box a little.
No news from Wales - I expect the status quo
Scotland - I think Labour will gain a lot of seats, at the expense of the Tories and the SNP
N.IReland - Unfortunately Sinn Fein will win, which will stir the pot a lot.