Markit's latest Purchasing Managers' Index (PMI) for manufacturing fell to 51.9 in April from 54 in March.
The pound slid 1.5% against the dollar to $1.5126 and dropped 1.1% against the euro to €1.352.
The FTSE 100 closed 25.32 points higher at 6,985.95.
After four months of 2015 the blue-chip index is up 6.3%.
Lloyds Banking Group was the top riser, jumping 7.1% to 82.87p after investors welcomed its first-quarter results.
Underlying profits at Lloyds rose 21% to £2.2bn, at the top end of forecasts, although the bank said it had taken a £660m loss on the sale of TSB to Spain's Banco Sabadell.
Mining stocks also bolstered the market, with Anglo American up 5.4% and BHP Billiton 3% higher.
The top faller on the FTSE was Aberdeen Asset Management, down 2.5% at 463.1p.
Outside the FTSE 100, shares in Hornby rose 1.7% after the model train maker said it was set to report an underlying full-year profit of £1.5m.
The company - which also owns the Scalextric and Airfix brands - said this would be the first time for three years that it had reported a pre-tax profit.
(Close): The FTSE 100 ended the week slightly higher despite a closely watched survey showing weaker-than-expected manufacturing growth.