The former It girl, who more recently appeared on I'm a Celebrity Get Me Out Of Here, had recently revealed a secret year-long battle with a brain tumour.
Doctors discovered the tumour in January last year.
Scotland Yard confirmed police were called by the ambulance service at 1.40pm today and the death is currently being treated as unexplained.
A spokesman said: "Police were called by London Ambulance Service at approximately 13:40hrs on Wednesday, 8 February to an address in Bramham Gardens, SW5.
"The death is being treated as unexplained. At this early stage, police are not treating the death as suspicious.
"Enquiries into the circumstances are ongoing. The Coroner has been informed."
Three months ago, the socialite explqined how she feared she was going to die when doctors revealed she had a brain tumour.
She said she had received treatment for the non-malignant growth in her pituitary gland since January 2016 and said at the time that it had cleared.
Her best friend Duncan James tweeted this afternoon: 'Heartbroken and numb I have lost one of my oldest and dearest friends. I'm going to miss ur laughter the most shmooey . Rip sweetheart.'
Piers Morgan wrote on Twitter: 'RIP Tara Palmer Tomkinson, 45. A fun, feisty woman who battled many demons. Very sad news.'
Grant Harrold, aide to Royals & former Butler to TRH Princes Charles, William & Henry also paid his respects.
He wrote: 'I am deeply shocked & saddened to hear Tara Palmer-Tomkinson has died. I was lucky enough to have met her and know her family. A lovely Lady.'
Tara's former I'm A Celeb co-star Darren Day wrote: 'I'm so sad to hear that Tara Palmer-Tomkinson has passed away. Thoughts and love to her family RIP Tara x.'