The table, compiled by International Financial Law Review, shows Linklaters advised banks on 41 international equity issues in the 12 months to the end of June this year, while Davis Polk, last year's leader, advised on 35.
But US firms Shearman & Sterling and Sullivan & Cromwell were joint second in the table, reflecting the continuing popularity of US markets such as Nasdaq and the New York Stock Exchange for companies making share offerings. It also shows the continued reluctance of US banks to instruct UK firms on US listings, despite their hiring of US lawyers.
US firms also showed continued dominance of their Latin American backyard, advising on 25 share issues between them. Of the UK firms, only Clifford Chance advised on one issue in Latin America.
Slaughter and May slipped from ninth position to twelfth. IFLR editor Paul Lee blamed its "lack of US lawyers and lack of foreign offices".
But David Frank, head of Slaughters' capital markets department, disagreed: "It's more to do with which of our clients are thinking of instructing us on an issue in the year. We work together with a US firm when US capability is required."
Most of Linklaters' deals were in Asia, where uncertainty in financial markets may lead to fewer deals.
Freshfields and Clifford Chance each doubled the number of transactions, to 18 and 14 respectively.
Freshfields and Allen & Overy became the first UK firms to advise on a full SEC registered listing in New York.
Freshfields' head of international equity, Stephen Revell, said its rise in deals reflected a deliberate strategy to build up US capability and invest in foreign offices "on the ground".
But US firms remained ahead in a separate table for advisers on European company issues. Shearman & Sterling topped the table, Sullivan & Cromwell came second, Allen & Overy third, Davis Polk fourth and Cleary Gottlieb Steen & Hamilton fifth.
Allen & Overy appears to be building strong links with merchant banks arranging issues in Europe - advising them on 18 issues but advising companies on only three.