Conditional dealings in Virgin Mobile will begin on 21 July with shares given a 235p-285p price range, the firm said.
Virgin Mobile gained full control from former partner T-Mobile in January
The move values the company, which will announce a final price for its global offering on 20 July, at £588m to £713m($1.08 to $1.32bn).
Virgin Mobile is the UK's fifth largest mobile operator with 4.1 million customers. It was launched in 1999.
As much as £279m raised by the listing will fund expansion within the Virgin group of businesses.
The company is selling 37% of the shares in Virgin Mobile in the initial public offering.
It is the first time Sir Richard Branson has listed one of his businesses in the UK in 18 years.
The company had been expected to come to the market after it gained full control from former partner T-Mobile in January.
T-Mobile sold its 50% stake in the firm to the Virgin Group to end a long-running legal row between the two sides.