The Art Fund, which is the UK’s leading independent art charity, kick started the appeal with a £100,000 grant towards the purchase. The galleries now have three months to raise a total amount of £420,000.

Currently in a private collection and rarely seen in public, the compelling portrait by one of the great artists of the late eighteenth-century, depicts Arkwright, the first of the 'cotton kings' in the mid-1780s when he was at the height of his wealth and power.

Arkwright was the father of the factory system on which the Industrial Revolution depended and the portrait brilliantly captures the self-made man who was later described as a ‘plain, almost gross, bag-cheeked, pot-bellied Lancashire man’.

In an early example of the ‘rags to riches’ story, Arkwright was born the son of a tailor in Preston and began life as a poorly-educated barber. The cotton-spinning frame, for which he is famous was invented in Preston in 1768 and patented in 1769.

By 1771, he had established his first water-powered cotton mill at Cromford in Derbyshire. There he developed a major industrial empire and is today acknowledged as the founder of the modern factory system. The year after this portrait was completed, Arkwright was knighted.

“This impressive and evocative painting is a fine example of Joseph Wright of Derby’s fascination with the leading industrial figures of the time,” said David Barrie, Director of The Art Fund.

“Despite being born in Preston, there is currently no portrait of him in the local museum and I’m delighted that this excellent example will now have the opportunity to join both the Harris Museum and National Portrait Gallery’s collections.”

The joint acquisition means each gallery needs to raise half the funds. The picture would not be subject to frequent movement but, over time, it would be seen in tellingly different contexts at each venue.