Lexington Communications is BA's retained public affairs adviser.
Cahn's exit comes as the carrier battles a black hole in its pensions fund of up to £2bn and amid concerns over rising oil prices – which have led to soaring fuel costs.
However, BA did recently post an increase in pre-tax profits, from £154m to £164m for the three months to December 2005.
CEO Willie Walsh, who replaced Rod Eddington on 1 October, is on a mission to bring about a leaner, more efficient business. He has already taken the axe to 600 managerial posts.
The airline's planned relocation to the under-construction Terminal 5 in 2008 has triggered speculation about further cuts down the line.
BA head of corporate communications Iain Burns revealed the managerial cuts would affect six or seven of his 38-strong comms team. He explained that the redundancies, which will be voluntary, apply to 50 per cent of senior managers (of which there are four in the PR department) and 30 per cent of managers (of which there are 15). The jobs will go over the next six months.
Cahn takes up his new role at UK Trade & Investment on 27 March and replaces Sir Stephen Brown, who retired in December.
Armed with a £280m budget, UK Trade & Investment supports British businesses trading overseas, and foreign companies looking to invest in the UK.