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The Rothschild heiress played out a marital row with Mr Goldsmith on Twitter with the pair publicly criticising one another over her affair with the US-born musician.
While Mr Goldsmith has reportedly moved out of the marital home, Miss Rothschild remains in their £20 million Kensington property but has also been staying with Electronica in his Chelsea flat.
They were photographed together with Miss Rothschild's rescue dog Faith as they set out to work.
She has previously said of Electronica: "He has saved my life in many ways" and criticised the backlash she faced over her fight with Mr Goldsmith.
But in recent weeks, it appears a truce has been called and neither have directed any further acrimonious messages towards the other.
The dispute came to a head when police arrested Mr Goldsmith, son of the billionaire banker Sir James Goldsmith, on suspicion of actual bodily harm.
It was reportedly a confrontation over Miss Rothschild's contact with Electronica, real name Timothy Elpadaro Thedford.
She later said her marriage "went bad a few years ago" and said no one had "any idea what I went through along with my husband". She had been in a relationship with Mr Goldsmith since she was 17.
As members of two of the most eminent banking dynasties, the pair will face a costly divorce as they carve up their assets.
It is also likely to cause further friction as Miss Rothschild's sister Alice is in a relationship with Mr Goldsmith's brother, Conservative MP Zac Goldsmith.
The Rothschild heiress played out a marital row with Mr Goldsmith on Twitter with the pair publicly criticising one another over her affair with the US-born musician.
While Mr Goldsmith has reportedly moved out of the marital home, Miss Rothschild remains in their £20 million Kensington property but has also been staying with Electronica in his Chelsea flat.
They were photographed together with Miss Rothschild's rescue dog Faith as they set out to work.
She has previously said of Electronica: "He has saved my life in many ways" and criticised the backlash she faced over her fight with Mr Goldsmith.
But in recent weeks, it appears a truce has been called and neither have directed any further acrimonious messages towards the other.
The dispute came to a head when police arrested Mr Goldsmith, son of the billionaire banker Sir James Goldsmith, on suspicion of actual bodily harm.
It was reportedly a confrontation over Miss Rothschild's contact with Electronica, real name Timothy Elpadaro Thedford.
She later said her marriage "went bad a few years ago" and said no one had "any idea what I went through along with my husband". She had been in a relationship with Mr Goldsmith since she was 17.
As members of two of the most eminent banking dynasties, the pair will face a costly divorce as they carve up their assets.
It is also likely to cause further friction as Miss Rothschild's sister Alice is in a relationship with Mr Goldsmith's brother, Conservative MP Zac Goldsmith.
