Nick Irens, the chief executive who founded the company two years ago after leaving as finance director of First Leisure, said he would prefer a site close to the Thames.
Mr Irens said the Sea Life concept would also appeal at inland sites, and that other centres could be built in Europe where the company has established a footing at Scheveningen in the Netherlands.
Vardon started in March 1992 when Mr Irens teamed up with chairman David Hudd to buy the London and York Dungeons. It bought Sea Life six months later, and last year bought into the bingo market.
Mr Irens, who yesterday reported taxable profits of pounds 5.13m for 1993, against pounds 2.16m the year before, said acquisition activity would continue at a more pedestrian pace but did not rule out the possibility of adding another side to the business.
'We have no immediate plans to make an acquisition of a third leg, but we have demonstrated our ability to make acquisitions and we would grab the opportunity if it was there,' he said.
Mr Hudd said Vardon would open two more bingo clubs this year to add to the 10 it bought in 1993. Despite the 960 clubs already operating in the UK, he said there were still opportunities to develop the market - particularly through edge-of-town sites.
More than 8,000 people a week are using its latest club in Southampton. 'We have expanded the market by 5,000, since we probably only took 3,000 away from competition,' said Mr Hudd.
In total, more than 4.6 million people used Vardon's facilities last year, of which 3.6 million visited the Sea Life Centres and dungeons.
Vardon's shares, floated on the stock market at 45p in October 1992, closed unchanged at 136p. The dividend is being lifted 50 per cent to 1.125p.
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