Waltham Forest Council has been attempting to deliver last-minute postal votes to residents this week that should have been out by last Friday.
An administrative error had reportedly delayed the process, affecting 1,470 voters in three constituencies, including Chingford and Woodford Green.
People across the country have until 10pm today to vote in today's General Election, the first to be held in December in almost 100 years.
The news comes after the elections watchdog warned that it may be an offence to share information obtained at postal vote opening sessions.
BBC reporter Laura Kuenssberg said that while parties are not supposed to look at voting papers when they are verified - but not counted - at opening sessions, they do "get a hint" of how they are doing.
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 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.”
A video of her remarks, made during an interview on the BBC's Politics Live programme, was widely shared on social media and appeared to provoke a response from the Electoral Commission.
The BBC said in a statement it did not believe Kuenssberg had broken electoral law in her comments.
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 and has apologised for the error and said the Electoral Commission had been notified.
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