The BBC has said its political editor, Laura Kuenssberg, did not break electoral law when she reported claims that postal ballots painted a “grim” picture for Labour.

Kuenssberg told viewers on Wednesday that while parties were not supposed to look at voting papers when they were verified – but not counted – at opening sessions, they did “get a hint” of how they were doing and it was not looking good for Labour.

She said: “The forecast is that it’s going to be wet and cold tomorrow. The postal votes, of course, have already arrived. The parties – they’re not meant to look at it, but they do kind of get a hint – and on both sides people are telling me that the postal votes that are in are looking pretty grim for Labour in a lot of parts of the country.

“Of course, postal voters tend to skew to elderly voters and people who vote early … but the kind of younger generation who we know skew much more to the Labour party, you might expect to turn out to the polls tomorrow. But in this winter election, turnout is just another one of these factors that we just can’t predict.”

Video of her remarks, made during an interview on the BBC’s Politics Live programme, was widely shared on social media on the final day of an election campaign that has seen unprecedented criticism of the media. It led to suggestions that she could potentially have breached the Representation of the People Act, which prevents the reporting of how people voted until after polls close.

A spokesperson for the broadcaster made clear they did not believe there were any issues with the on-air comments. “The BBC does not believe it, or its political editor, has breached electoral law,” they said.

Party candidates and agents can observe postal votes being verified before polling day but the ballot papers are placed face down and are not counted until polls close on election day.

In reality, political parties regularly use the verification process as an opportunity to try to divine information on how they are performing in constituencies and adjust tactics in the final days of the campaign.

This week BuzzFeed News reported claims that a northern Labour official had told colleagues that “postal votes in all Labour seats are bad” and ordered activists to stay in so-called defensive seats already held by the party.

In 2010 the Labour MP Kerry McCarthy infamously tweeted the result of the postal votes in her Bristol East constituency, for which she received a caution from the police.

The Electoral Commission issued a statement on Wednesday warning against revealing results. “It may be an offence to communicate any information obtained at postal vote opening sessions, including about votes cast, before a poll has closed. Anyone with information to suggest this has happened should report it immediately to the police,” it said.

The Guardian has learned that Waltham Forest council in east London has been scrambling to deliver postal votes that should have been out by last Friday, after an administrative error delayed the process.

The problem affected 1,470 voters in three constituencies, including Chingford and Woodford Green, which Iain Duncan Smith won for the Conservatives with a majority of 2,438 at the last election and which is a key target for Labour.

The council could not say how many voters were affected in each constituency but said all but one form had now been delivered.

It said 1,364 forms had been hand-delivered by the end of Monday and 105 more had been couriered to voters outside London on Tuesday and Wednesday.

A council spokesman said the borough had dealt with 27,993 postal votes for this election. He apologised for the error and said the Electoral Commission had been notified.

He added: “Completed postal votes will get to us if they are posted by last post on Wednesday 11 December. They can also be handed to staff at any polling station in the constituency on the day of the general election.”