Labour leader Ed Miliband has tweeted:
21 years ago John Smith set out on the journey of One Member, One Vote. Today we have completed that journey. #OneNationPolitics
Now the battle to change our party is over. The fight for the future of Britain has just begun. #OneNationPolitics
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Labour strongholds tended to remain so - apart from a major loss for the party in Dudley.
Labour suffered a "terrible" defeat in Rhondda but has already won 16 Welsh Assembly seats as it looks to record a fifth term in office.
UKIP have made further gains in the local elections in the Anglia region and the Conservatives have won back control in Peterborough.