He later told police he had travelled to the Nevada city to kill Mr Trump, the presumptive Republican nominee for the US presidential election, according to court documents.
Sandford’s mother has voiced fears that her son, who faces up to 30 years in prison if convicted, may try to take his own life in a US jail and called for him to be returned to the UK.
Lynne Sandford told the BBC’s Victoria Derbyshire: ‘I would like him to be deported so he can be back in the country and can get psychiatric help and that way he could see the family that still adore him.
‘Jail is no place for him. He needs help, but not prison.’
Mrs Sandford said her son had been diagnosed with Asperger’s syndrome when he was 13 and he had previously tried to kill himself. He had to be sectioned as a teenager after suffering from anorexia, she added.
Sandford, from Dorking in Surrey, has been charged him with one count of impeding or disrupting government business and official functions and two counts of being an illegal alien in possession of a firearm.
According to Nevada court documents, Sandford told a policeman at the rally that he wanted Mr Trump’s autograph before he attempted to seize the officer’s gun.
During a police interview, when asked why he attempted to grab the weapon, Sandford replied: ‘To shoot and kill Donald Trump,’ the document showed.
He had driven to Las Vegas from Californa on June 16, and went to a shooting range the next day, where he said he learnt how to use a gun for the first time, it is claimed.
Sandford – who had been living in the US for around 18 months – told investigators he expected to die in the attempt on June 18, which he had been planning for a year.
He also claimed to have booked tickets for another Trump rally in Phoenix, Arizona, in case he was unable to attempt to take the billionaire’s life in Las Vegas, the documents said.
Sandford, who is in custody, is due to be arraigned when he appears at the Lloyd D. George federal district courthouse in Las Vegas at 3pm local time.
She told the programme that Sandford had never spoken to her about politics.
‘As I have said he is a very gentle, very calm, person by nature and he would see there was no point,’ Ms Sandford said.
‘Why would he live the next 30 years in these situations? So yes, I think he would attempt to commit suicide again.’
She added: ‘I would like him to be deported so he can be back in the country and can get psychiatric help and that way he could see the family that still adore him.
‘Jail is no place for him, he needs help. But not prison.’
She said her son had been diagnosed with Asperger’s when he was 13 and had to be sectioned as a teenager after suffering from anorexia and coming close to dying. She added that he had previously attempted to end his own life.
Ms Sandford said her son had been visited in the US following his arrest by his father who spoke with him via video link.
She said Sandford’s father had told her their son had appeared ‘bewildered and disorientated’ and that he ‘didn’t seem to know what was going on around him or what the consequences were going to be’.
Ms Sandford said the 20-year-old was being held in isolation for 22 hours a day in a medium-secure facility with 1,100 other people.
Last month, US Attorney Daniel Bogden said a grand jury had charged him with disrupting an official function and two firearms counts.