The industrial trends survey from the Confederation of British Industry (CBI) also found companies expect price pressures to ease further.
Demand showed a solid improvement, with 17 per cent reporting order books were above normal and 28 per cent said they were below normal, leaving a net balance of minus 11 per cent.
That is a rise from minus 17 per cent in May, and is above the long-term average of minus 17 per cent.
Export orders drove much of the improvement – the balance improved from minus 12 per cent to minus four.
As a result, a net balance of seven per cent of manufacturers now expect output to increase in the next three months.
That represents a rebound from the balance of minus three per cent recorded last year – a sudden negative blip after four months of positive forecasts.
But despite the improvements in orders and outlook, economists warned the economy remains fragile, and said a strong recovery is not yet on the cards.
“UK manufacturers clearly face a very challenging domestic and international environment,” said Howard Archer from IHS Global Insight. “Domestic demand is handicapped by a still appreciable squeeze on consumers’ purchasing power as well as by tighter public spending.”
Meanwhile, Eurozone economic weakness, in particular, is limiting overall foreign demand for UK manufactured goods.”
The price expectations balance fell from 12 to two, its lowest level since November 2011, driven by falling oil prices – a factor which could lead the Bank of England to boost its quantitative easing programme in an effort to stimulate demand.