Sterling, which jumped last week on expectations of a BoE shift towards higher borrowing costs, fell after the Markit/CIPS UK Manufacturing Purchasing Managers' Index(PMI) slipped to 54.3 from a downwardly revised 56.3 in May, a three-month low.
The reading was below all forecasts in a Reuters poll of economists that had pointed to a reading of 56.5.
It also contrasted with a sharp pick-up in growth for factories in the euro zone.
Britain's economy barely grew in the first three months of the year, with consumers facing the double hit of accelerating inflation, caused in large part by the fall in the pound since the Brexit vote, and slowing wage growth.
Some BoE officials say the consumer drag on the economy is likely to be offset by higher exports and investment and two of the sitting eight monetary policymakers voted last month for a rate hike. A third supporter of a hike has since left the BoE.
However, Monday's survey suggested the supposed silver lining of a weak currency - more competitive exports - is proving elusive, even as the global economy picks up.
The PMI showed export orders rose last month at the weakest pace since January.
"While the survey data add to signs that the economy is likely to have shown stronger growth in the second quarter, further doubts are raised as to whether this performance can be sustained into the second half of the year," said Rob Dobson, senior economist at IHS Markit.
"Export orders remained disappointingly lackluster despite the ongoing competitiveness boost of the weak sterling exchange rate."
The EEF, a lobby group representing manufacturers, said the sector would probably provide a counterweight to a slowing in Britain's far bigger services sector, but employers were wary about the political outlook after Prime Minister Theresa May was left weakened by last month's inconclusive election outcome.
"The build-up in political uncertainty looks to be dampening sentiment in the sector somewhat," George Nikolaidis, an EEF economist, said.
An Institute of Directors survey published in June showed business confidence fell sharply after May lost her parliamentary majority the election.
Monday's PMI showed price pressures for manufacturing firms eased in June, which could help ease the squeeze on profit margins. However, optimism sank to an seven-month low.Among investment goods manufacturers, who are critical to the recovery in investment expected by the BoE, optimism fell to its lowest level since last July.