Elsewhere in London, Labour failed where they should have succeeded.
He wrote on Twitter: "Almost everywhere that @PeoplesMomentum held #Unseat campaign events, Labour made gains - some big - and the Tories lost seats".
He took over as Tory leader from former Barkingside Councillor Keith Prince in May 2014, who resigned shortly after Labour gained a majority for the first time in the council's 55-year history.
Analysis suggested the two main parties were neck and neck overall in terms of national vote share - on 35 per cent each.
"Even Donald Trump received a greater share of the minority vote in the presidential elections than the Tories achieved in last year's general election".
However, he insisted it was a "solid set of results" which left the party "well placed to fight and win the next general election".
The Conservatives are widely seen to have benefitted from the collapse of the UKIP vote - prompting leading Brexiters such as Boris Johnson and Iain Duncan Smith to urge the prime minister to press on with plans for a clean break with the EU.
Mr Corbyn sought to put a fearless face on overnight results which saw Labour pick up more than 50 seats but gain control of only one council, in Plymouth.
Mrs May praised Tory councillors after winning Basildon, Peterborough and Barnet.
On Friday night Tower Hamlets became the last council to declare, with Labour the victor.
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With all councils declared, Labour won 2,350 seats, up 77, the Conservatives won 1,332, down 33, the Lib Dems won 536, up 75, the Greens won 39, up eight and UKIP won three, down 123. But they have lost control of their northern flagship Trafford Council after 14 years of Conservative rule.
- The Liberal Democrats put on an extra 76 seats and gained control of four extra councils.
The Greens have gained seats - taking some from Labour in Sheffield and from the Tories in Richmond upon Thames. This time last week, the Conservatives were [1.9] to win most seats next time Britain goes to the polls.
Many commentators pointed to the Conservative win in Pendle council in the North West as proof that Labour were being punished by the electorate up North.
Labour MP Dan Jarvis has been elected mayor of the Sheffield City Region. A dispute over the handling of anti-Semitism in the party may have also cost support for Labour and Mr. Corbyn, particularly in Barnet, where there is a significant Jewish population.
"Therefore, above all, it seems to me that what the Conservative Party has to be able to do in the coming weeks and months is to deliver on Brexit in a way that will satisfy the aspirations of "Leave" voters", he said.
Shadow justice secretary Richard Burgon denied that Mr Corbyn's response to Syria and the poisoning of the Russian spy in Salisbury were issues on the doorstep for traditional Labour voters.
"It's not all over at all", Mr Oakley told BBC Radio 4's Today programme.
"Here's a councillor who brought shame on the borough on an worldwide level and was welcomed back into the fold with open arms simply to grab control to the council", said Labour group Cllr Mohammed Iqbal.
"So what I would say back to Ken Livingstone and others who have made this argument that it's all a smear created to just undermine Jeremy Corbyn, let's hope that these elections draw a very firm line under these arguments and basically knock it out, because the truth of the matter is there is a very real sense of rawness in the Jewish community".
Thursday's results mean Theresa May is not in danger of facing an immediate leadership challenge - as she might have been had things gone really badly.