Speaking to the BBC while on a visit to a school, Ed Miliband says there are "wider lessons" to learn from this by-election.

"We know we've got a challenge in relation to UKIP. It's a challenge I'm determined to meet," he vows.

Asked how he would meet that challenge, Mr Miliband replies: "I think what it says is there is deep discontent about the country and there is also scepticism about whether any mainstream party can turn it around.

"Our fight, our job, is to show we can."

The BBC's Westminster team reports that the man whose house was photographed by Emily Thornberry in that controversial tweet is thought to be heading to the Labour MP's Islington constituency with a large flag.

Ed Miliband has also been speaking about the tweet sent by Labour's Emily Thornberry. He says it "conveyed a sense of disrespect" and "that's why I was so angry about it".

Mr Miliband says her intention "may not have been" to be disrespectful but adds: "I was angry because I thought her tweet gave a misleading impression, when she photographed the house in which the family lived, that somehow Labour had the wrong view of that family.

"It's not the view we have of that family. Labour's never had that view, of disrespect."

Labour leader Ed Miliband tells the BBC: "I think the most important thing about these results is that it was a devastating result for David Cameron."

He adds that in his view the Conservatives "lost and lost badly".

Also in that interview with Nick Robinson, Nigel Farage gave some more details about the policies his party would pursue.

He said he "obviously" favoured tax cuts, "particularly for the low paid, the idea that anyone earning minimum wage is paying income tax is crazy".

He denied he had ever spoken in favour of more privatisation of the NHS, adding he wanted to see fewer private companies involved in the NHS as it "hasn't worked - all it's done is transfer money out of public sector to make rich people richer".

Former Conservative - now UKIP - MP Douglas Carswell says the Conservative Party has plenty to ponder following the by-election result.

He said: "If the Conservative Party think that all is well then they've got an even bigger problem than the rest of the country thinks they've got.

"Britain today is a country where pretty much everything is run in the interests of vested interests. Politics, banking, the energy markets - they're all run by this self-serving little clique at the top."

Nigel Farage has told BBC Political Editor Nick Robinson he believes the number of seats UKIP can win in next year's general election has "probably doubled" following the by-election result in Rochester and Strood.

He refused to be drawn on whether UKIP would support David Cameron or Ed Miliband in any possible coalition agreement, saying UKIP would do a "deal with the devil" if it meant they could get what they want.

When asked if his party supported spending cuts or spending increases, the UKIP leader said: "Spending cuts and here's why; I think one of the real elephants room of British politics is that by at end of lifetime this parliament of national debt will have increased by 40%."

Ed Miliband's newly appointed campaign deputy, Lucy Powell, tells the Daily Politics that her colleague Emily Thornberry's tweet was "an insult" and although there were "question marks over what she wanted to say" her behaviour had been "unacceptable".

She rejected claims Labour was alienating its traditional base of working-class voters.

Al Scott from Brighton tweets, external: #Rochester Unintended mistake no doubt, but UKIP gain from common belief that Labour elite despise the very people they claim to represent.

Here's the moment veteran Labour MP Dennis Skinner gave UKIP's new MP a hard time mere moments after he was sworn into the Commons. He passionately accused Mark Reckless and his UKIP colleague Douglas Carswell of wanting to deport foreigners.

Continuing his interview on the Daily Politics, Mr Gove says voters were sending a message to the government that it needs to "sharpen up" and that the Conservatives have heard the message.

Asked if he did enough as chief whip to prevent Mr Reckless' defection, Mr Gove replies: "If people choose to say one thing and do another they say there's very little I - or anyone else - can do."

Eddie Eldridge from Gloucestershire tweets, external: One reality from #RochesterandStrood is that Tory pledges on Europe were simply not believed. Cameron needs to get that referendum rolling

Michael Gove, the government chief whip, tells the Daily Politics it was "a very good result - governments don't tend to win by-elections". He says "most dramatic thing has been the haemorrhaging of the main opposition party".

Following the Rochester and Strood by-election results, John Baron, MP for Basildon and Billericay, says the Tories are the only party to be trusted to hold an EU referendum.

"The fact remains that only the Conservatives are willing and able to deliver a much-needed in/out referendum after the next general election. The Labour and Liberal leaderships won't, and UKIP can't.

"Despite their many broken promises about referenda, Labour and the Liberals should be ashamed they arrogantly do not trust the electorate to make the right decision on this very important issue. A referendum is essential."

Chris Jones from Liverpool tweets, external: Interested in relatively low turnout in #RochesterandStrood, only just over 50% with about 7k voters less than general election.

Patrick O'Flynn, UKIP MEP, is on the Daily Politics this lunchtime. He dismisses the idea that a vote for UKIP is a protest vote and people will revert to larger parties at the general election as "a comforting narrative".

Pressed on whether there will be further defections, Mr O'Flynn says: "I really don't know. I know there are MPs seriously considering their positions."

On the furore over Emily Thornberry's tweet, Seb Payne from the Spectator says Labour leader Ed Miliband's reaction seemed "panicked" because he was rushing "to do something not to seem weak", and it was not the right decision for her to leave her front bench post.

SNP MP Pete Wishart tweets, external: My advice to the W'ster establishment parties is don't attack UKIP in the House like they do the SNP. It'll help them like it has helped us.

Seb Payne, online editor of the Spectator, tells BBC Radio 5 live the Conservatives "were always going to put that spin on it - that they haven't done as badly as expected", but points out conversely UKIP did not do as well as expected.

He predicts Mr Reckless "is going to struggle" in the 2015 as he doesn't have as great a margin of victory or as close a personal following as the other UKIP MP, Douglas Carswell.

Tory MP Mark Field tells the BBC that the situation was "disappointing" for the Conservatives.

He added: "In many ways, the appeal [of UKIP] isn't Europe or immigration alone, it's a cultural two fingers up to the entire political process. That's something all politicians have to be aware of."