The company said its recently-completed acquisition of Oakwood Underwriting Agencies, creating the largest names' agency at Lloyd's, reflected its view of the market.
With about 1,300 active names, Sedgwick Oakwood, as the agency is now known, represents about 10 per cent of Lloyd's membership and the same proportion of underwriting capacity.
Sax Riley, chief executive at Sedgwick, said: "Lloyd's continues to make good progress towards a resolution of its major issues and there is a growing feeling of optimism.
"The recent news that the Californian authorities are to permit Lloyd's to communicate reconstruction and renewal information to Californian names makes us feel even more positive about the eventual outcome."
Brokerage and fees increased at Sedgwick from pounds 234.4m last year to pounds 243.2m in the first three months of this year. However, expenses, at pounds 209m, remained broadly flat. Shares prices rose 3p to 149p on the announcement of the results.
Mr Riley added: "Conditions remain tough across most sectors of our business and we continue to take the necessary measures to enable us to compete in today's markets.
"In insurance broking, markets remain intensely competitive, with particular pressure on rates in Europe. In North America, business is developing well and is supported by a high level of business retention."
He said long-term prospects for Sedgwick Noble Lowndes, the company's financial services arm, were also bright, particularly in the rest of Europe, where the provision of many employee benefits is moving to the private sector.
In the UK, the company's new business activity had also increased in the past three months, reflecting a mood of growing confidence among consumers, increasingly prepared to consider long-term financial planning in investments, life and pensions products.