Scotland Yard confirmed the 55-year-old's death was not being treated as suspicious.
Ms Woodall, who is dating Nigella Lawson's former husband Charles Saatchi, was said to be devastated by his death.
The former couple battled drugs and alcohol addiction throughout their marriage and remained friends after their split in 2009.
Mr Elichaoff regularly featured on the Channel 4 programme Four Rooms. In the series, members of the public pitch weird and wonderful objects to professional dealers. Mr Elichaoff was one of the dealers on the programme.
Westminster Coroner's Court in London confirmed they may open an inquest next week.
A Met Police spokesman said: 'Officers and London Ambulance Service attended the scene. The man, believed aged 55, died from his injuries at the scene.
'Next of kin have been informed. At this stage the death is not being treated as suspicious'.
Alex Fakhre, 25, who witnessed the fall, told the Evening Standard: 'I was coming back from my girlfriend's and the road was all blocked off. The police said a guy had fallen from the car park (roof). He looked in a pretty bad way.'
A source told The Sun Miss Woodall, 50, was 'grief-stricken' by the loss of her former partner.
Her ex-husband's family are also too upset to speak.
The pair married in Knightsbridge in 1999 at St Columba's church where Miss Woodall was christened, her parents had married and her grandfather was buried.
Trinny's wedding dress was made by designer Elspeth Gibson, but she created the designs for her bridesmaids' dresses, while their shoes were made by Christian Louboutin and differed according to the shape of the bridesmaids' ankles.
Back in 1982, it was Johnny who first found fame, as a madcap rock drummer who toured the world supporting U2 and Siouxsie Sioux.
Nicknamed Johnny Too Bad, he played in a Seventies band called Stark Naked And The Car Thieves before defecting to the equally bizarrely named Baby And The Black Spots and then playing in guitarist Robert Fripp's League Of Gentlemen.
His musical career was interrupted by a two-year spell in the Army in 1984, and he went on to help manage rock bands Tears For Fears and Fairground Attraction.
But the musician changed his career to become a financial adviser.
However, he developed an addiction to prescription painkillers in 2006 when he had 20 operations after breaking his leg in a motorbike accident.
He was then treated in a Californian rehab clinic in October that year.
Following their split in 2009, the couple remained on good terms. They would regular dine out together with their daughter Lyla.
Friends said the marriage had broken down partly because of Miss Woodall's busy work schedule but his dependence on painkillers proved a strain.
Mr Elichaoff suffered from an addiction to prescription painkillers. Miss Woodall also had her own battle with substance and alcohol abuse. The couple have both spoken openly about their issues.
A friend said Trinny felt 'let down' that he did not make the same inroads she did.
He said of his wife before their divorce: 'Trinny comes across as cold and aloof, but in fact she is the kindest woman I have ever met. She has a heart of gold. The steeliness people see in her is really a cover for her chronic shyness, believe me.'
Last year, during talk hosted by The Spectator magazine, Miss Woodall talked publicly about her battle with cocaine and alcohol.
She said: 'I'm Trinny, I'm an alcoholic and I'm an addict. When asked whether addiction is a disease, I didn't have to think twice. Knowing that I have a disease is how I manage to have a healthy life today.'
Trinny's work parter Susannah - married to Danish entrepreneur Sten Bertelsen and the mother of their three children - fell into motherhood effortlessly.
But Trinny was diagnosed with blocked fallopian tubes and endured nine rounds of IVF and two miscarriages before she conceived.
This was said to have put pressure on her marriage to Elichaoff.
She said at the time: 'It is stressful having IVF. I'm a hormonal cow for a month, but luckily my husband is very patient.'
When she finally became pregnant she spoke glowingly of Johnny. 'I still feel a sexy woman, which is important,' she said.
'Some husbands are very funny about their wives when they're pregnant and go off them sexually, but my husband never puts me down. I'll say, 'I hate my thick legs,' and he'll say, 'Trinny, you can cover them - and your t*** look fab.' He always makes me feel great.'
Of all the storms they weathered, it was said Trinny's struggle to become pregnant was the toughest.
Miss Woodall began a relationship with Charles Saatchi, 71, in the summer of 2012, eight weeks after he split from his former wife, Nigella.
The couple's 10-year marriage ended after Mr Saatchi was photographed clutching the celebrity chef's neck outside Mayfair restaurant, Scott's - one of the art dealer's favourite haunts.
This summer, less than 12 months after the incident, Miss Woodall was pictured with Mr Saatchi sobbing at a table outside the same restaurant.
Confirming Mr Elichaoff's death last night, a Channel 4 spokesman said: 'Our thoughts are with his friends and family'.
- Daily Mail
