Alice Beer, who worked alongside Dando on the BBC’s Children in Need and Holiday programmes, said she received the sinister letter in her BBC mail, which bosses had passed on to police.
But the 49-year-old said she had not been interviewed by officers either before or after Dando was shot dead outside her home in Fulham, west London, in April 1999.
Barry George, from Fulham, was convicted in July 2001 of killing the 37-year-old presenter but was acquitted at a retrial in August 2008.
Beer said: “There are a lot of questions I would like answering. They’ve been at the back of my mind. I waited for a call from the police after Jill’s death, but it never came. Nobody spoke to me about the threat.
“Nobody questioned anything. If no stone were left unturned in that investigation, then I would have been called.”
Now a presenter on ITV’s This Morning, Beer was working on BBC consumer programme Watchdog when she received the threats in March 1999.
Her colleague on the show, Anne Robinson, received a death threat by phone three days after the killing, which reportedly said: “From Serbia, going to kill Anne Robinson, Alice Beer and two others.”
The call was said to have been traced by police to a phone box in Gerrards Cross, Buckinghamshire.
Beer said she believed the threat to her had been written by the same person who threatened Dando.
She said: “The letters were in the same handwriting from a person claiming they wanted to capture and rape us.
“Mine was in amongst my mail at the BBC. My letter was handed over to the police via the programme editors or the management of the BBC. I was told Jill Dando had had a similar letter in the same handwriting and the local Shepherd’s Bush police were investigating.
“So when Jill was shot a month later, that was in the back of my mind – that somebody had threatened both of us in handwritten letters not long before she was murdered. Yet I never received any contact [from police].”
The murder had been a “slick” and “professional” , she added.
Beer said: “My first thought when we heard what had happened was ‘Why Jill?’ She was the very last person anybody would have wanted to murder – an absolutely lovely positive person. I never heard anyone say anything nasty about her at all.
“These are busy, noisy streets, and for somebody to shoot in broad daylight, escape and dispose of the murder weapon, that’s an incredible feat.” A spokesman for Scotland Yard said: “The Metropolitan Police Service fully investigated the circumstances of the murder of Jill Dando. Two trials took place and the investigation was subject to an internal review.
“If any new information comes to our attention then this will be investigated.”
Barry George was arrested within a month of Dando’s murder and convicted the following year. He lost repeated appeals until the original conviction was quashed and a retrial ordered. A jury found him unanimously not guilty in 2008 but Mr George lost a bid for compensation in 2013.
Serbian assassins were linked to the murder in reports last year. At the time of the murder, it was the largest criminal investigation since the hunt for the Yorkshire Ripper.
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