The listing, which is believed to be the second largest of the year, raised £80m at an offer price of 100p per share. Shares are due to start trading on 21 October.
Addleshaw Goddard partner Clare Thomas advised nominated advisor Fox-Pitt Kelton.
Guernsey-registered company Burford will primarily target litigation in the US where the market is considered to be more buoyant.
Burford is chaired by Sir Peter Middleton, a former Treasury civil servant who chaired Barclays between 1999 and 2004. The company is led by former Time Warner general counsel Christopher Bogart and former Latham & Watkins senior partner Selvyn Seidel.
The listing will create the largest litigation investment company in the world. Primarily such companies operate in the US market, where the litigation model is believed to be more suited to independent funding.
Nevertheless, the UK funding market is beginning to take hold with a number of firms signing up to delegated authority deals with legal expenses underwriters.
In September Mishcon de Reya launched a range of alternative funding packages branded Mishcon Protect that are aimed at cutting costs by reducing the amount of time it takes to place insurance for a case operating on a conditional fee arrangement (28 September 2009).