In an upbeat statement to shareholders at the company's AGM, chairman Sir Brian Pitman said the three-month period to the end of March had seen profits and volumes well up on the first quarter in 1998.
Lloyds TSB, whose credit card services operation is based in Brighton, is already thought to be Europe's most profitable bank.
Sir Brian said it was "well on track" to meet its promised £400 million annual cost savings by the end of the year.
And, he said, the group was also still committed to a further cut in costs next year.
That will be beyond the £400 million already promised when Lloyds announced its merger with TSB in 1995.
Sir Brian added that a slowdown in both the world and UK economies was anticipated during 1999.
"We do not expect a hard landing and we remain confident of our ability to continue to produce superior returns for our shareholders."
In June last year Lloyds TSB announced a major expansion to its Brighton call centre operation, creating more than 400 new jobs.
The company is due to release its full figures for the first quarter of the year in August.
Figures for 1998, published in February, showed the bank reporting pre-tax profits on continuing businesses ahead at £3.29 billion - an increase of 14 per cent on the previous year.
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