Cox expects to have 1, 000 high street branches by the end of 2004 through acquisitions, according to chief executive Neil Utley.
He reinforced the insurer's commitment to the intermediary market and expanding its distribution.
"You have to remember that 40% of the motor market is broker-led. Plus we have to believe in networks because that is what HML (Cox's own broker network) is.
"If I had known HHH was on the market, I would have tried to buy it," said Utley.
He allayed broker fears that he intended to exit Lloyd's and integrate Equity Red Star into Highway if the acquisition was successful.
He said that Lloyd's "was very commercial in the way it helped us ring-fence the business" two years ago and its brand helped "support many of our big fleet motor customers who pay more than £1m for cover".
Overall, 2003 was a successful year for Cox. Profit before tax was up 22% to £52.1m from £42.7m in 2002. Underwriting profit on continuing business was up 32.7% to £52.7m from £39.7m in 2002.
Equity Red Star remained the jewel in the crown, with gross written premium up 5.5% to £556m from £527m the previous year. Utley said he expected Boncaster to grow further.
"It has done very well particularly as it's up against direct writers. The affinity schemes business it specialises in is a tough market."
The only glitch was Tribune Risk and Insurance Services, which went into liquidation in December 2003. Utley admitted the insurer was "caught out" by the failure, which cost it £4.5m.
"We reacted as quickly as we could with the liquidator and the FSA to notify Tribune customers."
He said: "So far 7, 000 customers have moved to us. It was not as bad as it could have been. It's one we can afford."
