Labour's overwhelming victory in the Oldham by-election shows how "strong" the party is, Jeremy Corbyn has insisted.

Ukip failed to make widely-predicted advances in the poll, clearing the way for the Labour leader to pass his first electoral test with flying colours as Jim McMahon held the seat with a majority of more than 10,000 despite divisions within the party in the days leading up to the poll.

But Nigel Farage has said he will file a formal complaint over alleged "abuses" in the Oldham West and Royton vote.

Speaking at a victory rally in Oldham, Mr Corbyn said: "This campaign shows just how strong our party is not just here in Oldham but all over the country. It shows the way we have driven the Tories back on tax credits, police cuts, on their whole austerity agenda and narrative.

"It shows just how strong, how deep-rooted and how broad our party, the Labour Party, is for the whole of Britain."

Mr Farage said he was not questioning Labour's victory, but denounced the electoral process as "bent" after claims that people had arrived at polling booths carrying bundles of postal votes.

The Ukip leader said the result raised questions about the conduct of elections in areas with large ethnic minority communities and claimed that in constituencies with large numbers of minority voters who do not speak English "effectively the electoral process is now dead".

Mr Farage told BBC Radio 4's Today programme: "There are some really quite big ethnic changes now in the way people are voting. They can't speak English, they have never heard of Ukip or the Conservative Party, they haven't even heard of Jeremy Corbyn.

"I'm commenting on the state of modern Britain, post mass immigration. It means effectively that in some of these seats where people don't speak English and they sign up to postal votes, effectively the electoral process is now dead."

Mr Farage claimed to have "evidence from an impeccable source that today's postal voting was bent".

Mr McMahon polled 17,209 votes, with Ukip's John Bickley trailing in second on 6,487, a majority of 10,722.

Labour's share of the vote increased by more than seven points to 62.1% in the by-election, triggered by the death of former minister Michael Meacher, and there was a 2.27% swing from Ukip to Labour.

Turnout was higher than expected at just over 40%, and Labour's success appears to have been partly secured by an effective postal vote operation.

Labour deputy leader Tom Watson said Mr Farage's comments appeared to be a case of "sour grapes".

"If he has got evidence of that, he should have told the police immediately," Mr Watson told Today.

"I have spoken to our organisers and they have got no knowledge of that."

Mr Watson said: "If this was a referendum on Jeremy Corbyn, then he has won. It was a decisive victory with our share of the vote going up.

"I hope our MPs look at this result. What's happened since Jeremy became leader and I became deputy leader is we have focused on issues that affect the working people of Britain.

"I think people responded to that at the ballot box. I hope our MPs will see that if you stand up for working people, they respond by supporting you at elections."

Westminster's newest MP - the leader of Oldham Council - said he was "delighted" by the result and vowed to "do my best to live up to those high standards" set by Mr Meacher.

Mr McMahon said: "The sooner we kick the Tories out and get a Labour government back in, the better for all of us. The hard work starts now."

Tory James Daly was third with 2,596, 9.37% of the vote, while the Liberal Democrats lost their deposit after Jane Brophy secured 1,024 votes, a 3.7% share.

Chancellor George Osborne offered Mr Corbyn his congratulations over the Oldham result in person, after they bumped into one another on a train.

In a tweet, Mr Osborne said: "Good to be one of the first to congratulate Jeremy Corbyn in person on his Oldham win - we're on the same train to Manchester this am."