Sabre's shares rose to 253 pence in early trade, having priced at 230 pence a share. The listing comprised 125 million shares, or 50 percent of Sabre's share capital, it said.
Founded in 1982, Sabre generated gross written premiums of 197 million pounds in 2016 and intends to maintain its focus on the UK private motor insurance market.
Sabre's listed rivals include Admiral, esure and Direct Line, which trade at between eight and 12 times core earnings, according to Thomson Reuters Eikon.
Motor insurers had come under scrutiny after a change to the way personal injury claims are calculated, which pushed up the size of those claims and dented insurers' profits.
However, Britain announced plans in September to change the rate for calculating personal injury payments, a move expected to cut the size of the payments.
Barclays and Numis Securities Limited are acting as joint global co-ordinators on the deal.
Sabre's private equity owner BC Partners had looked to list the Dorking-based company in London following an unsuccessful joint approach from U.S. investment firm Centerbridge and Qatar Reinsurance Company, sources told Reuters in September.
BC Partners took a majority stake in Sabre, which is behind the Insure 2 Drive, Go Girl and Drive Smart brands, in 2013 in a 240 million pound deal.
(Reporting by Noor Zainab Hussain in Bengaluru, editing by Louise Heavens)