The SNP have won an "historic" third victory in Scottish Parliament elections - but do not have enough seats to form a majority government.
Labour have been pushed into third by the resurgent Scottish Tories with the Greens beating the Lib Dems into fifth.
Deputy leader Tom Watson called it a "mixed picture" for Labour as Jeremy Corbyn's party held key councils in England, although it lost councillors.
UKIP is set to win seven Welsh Assembly seats on a good night for the party.
With all the results now declared in Scotland, the SNP is the largest party with 63 seats, ahead of the Conservatives on 31 and Labour on 24.
Labour is set to remain the dominant party in Wales but expected to fall just short of a majority. Counting continues across English councils with the London Mayoral result and Northern Ireland counting and results not expected until later on Friday.
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As it became clear there had been a third successive victory for the SNP, leader Nicola Sturgeon told supporters: "We have made history."
However Ms Sturgeon may have to do a deal with another party - probably the Greens, which have won six seats.
Analysis by Laura Kuenssberg, BBC political editor
Jeremy Corbyn's party has swerved universal disaster - losses so far in England are fewer than some had feared. But with meltdown in Scotland, and losses where there should traditionally be gains, Labour would be foolish to take much comfort from the results.
There is little to suggest that voters believe the Labour Party on its current performance is on its way to a general election victory. Mr Corbyn's internal enemies are not likely to wield the knife, but there are already calls for more decisive leadership, more appeals to go to the centre ground.
But nor is there much evidence of enthusiasm for the Conservative government in England. The Tories so far have picked up a handful of seats, traditionally an achievement for a party in power at these kinds of polls.
But for success, and unexpected success, the Conservatives can look to Scotland where it appears they are set to take second place, - a fundamental change in Scotland. But there, voters again expressed their faith and belief in the Scottish National Party as their government.
Read more from Laura
Much attention has been on how Labour did in the elections across Britain - and whether the party would do well enough to avoid a challenge to leader Jeremy Corbyn.
In the English council elections, BBC analysis suggests the Tory vote is down in southern England, which may have helped Labour to retain control of councils in areas such as Crawley, Southampton, Norwich and Hastings, where its vote was looking vulnerable.
Labour's vote share is down about 6% on average on 2012 - the last time these seats in England were contested - but a BBC analysis suggests its share is up 4% on the general election in key wards, with the Conservatives down by a similar amount.
Its share was more sharply down in Scotland. The party gained one seat from the SNP - Edinburgh Southern - but Scottish Labour leader Kezia Dugdale was left relying on the top-up system for a seat, after failing to take Edinburgh Eastern and being beaten into third place by the Conservatives in Scotland would have been unthinkable in the past.
Labour also lost its Rhondda Welsh Assembly seat, in its south Wales heartlands, to Plaid Cymru leader Leanne Wood.
In other developments:
- Former Tory MP Neil Hamilton among UKIP candidates elected to the Welsh Assembly
- UKIP gains English council seats, including six seats in Thurrock UKIP, and comes second in two by-elections
- Gill Furniss, the widow of Labour MP Harry Harpham, retains his Sheffield seat in a by-election
- The Lib Dems regain ground in Scotland, winning six seats including Willie Rennie taking a seat from SNP
- Liverpool Mayor Joe Anderson is re-elected
- Shadow Home Secretary Andy Burnham considers running for newly created role of Greater Manchester mayor
Brighter news for Labour came with it holding the seat of Sheffield Brightside in a Westminster by-election, on a 5.8% swing from the Conservatives, with UKIP coming second. The party also held Ogmore in another Parliamentary by-election, in South Wales, with UKIP again in second place.
Responding to claims Labour was not doing as well as it should be, deputy leader Tom Watson said Jeremy Corbyn still had a "very strong mandate" and needed "more time" to show he could revive its fortunes in time for the 2020 general election.
"After eight months it would be very unfair and actually improper to hang this set of election results on Jeremy Corbyn's peg alone," he told BBC Radio 4's Today.
Shadow environment minister Clive Lewis said it was time for critics of Mr Corbyn to "shut up or get out" but one senior MP told the BBC Mr Corbyn was seen as "weak" and had a year to shape up.
For the Conservatives, the most eye-catching moments so far have been in Scotland, winning the Holyrood seat of Eastwood from Labour and Scottish Conservative leader Ruth Davidson winning Edinburgh Central from the SNP.
Conservative Commons leader Chris Grayling told the BBC Ms Davidson had been successful because there was "no other political leader in Scotland who is so closely associated with the unionist cause".
Ms Davidson said: "There are people right across Scotland who are sending the SNP a message - the voices and the decision we made as a country will not be ignored."
The Lib Dems held Orkney and Shetland and took Fife North East from the SNP. The SNP took Rutherglen from Labour.
In a surprise result in Wales, Plaid Cymru leader Leanne Wood unseated Labour's Leighton Andrews in the Rhondda - described by former Labour cabinet minister Peter Hain as "a terrible shock for us in Welsh Labour".
Ms Wood said: "A new dawn has already broken over the Valleys, people have voted for change."
In Wales, Labour's vote is down by eight points overall, the Conservative vote is down by three points, while Plaid Cymru is up by two points.
UKIP has seen its vote increase by 12 points, suggesting it will maintain the level it achieved in 2015 which should be enough to enable the party to win its first assembly seats.
Image copyright PAIn total, 2,747 seats in English councils - spanning metropolitan boroughs, unitary authorities and district councils - were up for grabs. The majority of the seats were last contested in 2012.
Thursday's polls are the single largest test of political opinion before the next general election, which is scheduled for 2020, with 43 million people entitled to take part.
What to expect when (all timings are estimates)
Friday 6 May
Around 80 English local election results expected overnight
Scottish Parliament - results in all 129 seats expected overnight
Welsh Assembly - results in all 60 seats expected overnight
Liverpool mayoral result also expected overnight.
11:30 First results from around 50 councils in England to declare on Friday
15:00 First results of London Assembly elections
17:00 First preference vote share information for elections to Northern Ireland Assembly
1800 Result of first preference votes for Mayor of London (final result expected early evening)
Results of Police and Crime Commissioner elections in England and Salford mayoral contest are also expected on Friday.
Saturday 7 May
14:00 Results from five remaining councils in England
16:00 Result of Bristol Mayoral contest
Result of elections to Northern Ireland Assembly expected
Sunday 8 May
16:00 Result of elections to Bristol Council (final council in England to declare)
Results of Police and Crime Commissioner elections in Wales