Their wealth rose by 14% over the past year to a record £658bn, it shows.
Brothers Sri and Gopi Hinduja, who invest in property, healthcare and oil and gas, top this year's list with £16.2bn - up £3.2bn on 2016.
The list includes a record number of British billionaires - 134 - with 14 ones emerging over the last 12 months.
List compiler Robert Watts said: "While many of us worried about the outcome of the EU referendum, many of Britain's richest people just kept calm and carried on making billions."
He said a revived stock market had been behind the surge in wealth for the super-rich.
"We expected to see a chilling effect in the run-up to the EU referendum, but that simply did not materialise," Mr Watts said.
"A buoyant stock market usually drives the wealth of rich-listers higher, and since last June equities have soared."
Of those in the top 20, only the Weston family - Guy, George and Galen Jr - lost money in the last year.
They saw their fortune drop by £500m to £10.5bn because of a fall in the share price of Associated British Foods, in which they have a 20.8% stake.
The largest increase in wealth went to steel magnate Lakshmi Mittal, who added more than £6bn to his £13.23bn valuation.
However, he remains a long way from his 2008 peak of £27.7bn - a Rich List record.
Others on the list include:
- The Duke of Westminster - 26-year-old Hugh Grosvenor - is the only British-born billionaire in the top 10. He became the world's richest under-30 when he inherited the family estate last year
- Alisher Usmanov, who owns 30% of Arsenal Football Club, added more than £4bn to his £11.79bn fortune
- Brexit supporter Sir James Dyson, who last year became the first self-made Briton to break the £5bn barrier, this year increased his wealth to £7.8bn
- Zlatan Ibrahimovic, was the highest new entrant among sports stars with £110m after his move to Manchester United
- Adele consolidated her position as Britain's wealthiest ever female musicianby earning £40m, bringing her assets to £125m
Mr Watts said: "We're seeing more and more diversity in the composition of the Rich List.
"More women, more people from ethnic backgrounds, and more from surprising walks of life, with egg farmers and pet food makers lining up with hedge fund managers and private equity barons."
It now takes assets of £110m to break into the ranks of the richest 1,000 people in the UK. The figure in 2016 was £103m.
The top 20 in the list alone are worth a total of £191.77bn, increasing their wealth by £35.18bn over the past 12 months.