Watches of Switzerland operates shops under its own name as well as branded boutiques for luxury watch makers including Rolex, Omega, TAG Heuer and Breitling.
The company also owns the watch and jewellery retailers Mappin & Webb and Goldsmiths in Britain, as well as Mayors and Betteridge in the US.
Watches of Switzerland is the latest luxury company to voice their opposition to the tourist tax, with the chief executives of Burberry, Harrods and Harvey Nichols also attacking the policy.
Mr Duffy said: “The airport should be a good environment for luxury stores. People have the time, they feel good because they’re off on holiday, and we all spend more money when we’re off on holiday.”
Despite vocal opposition, Mr Duffy said it does not “seem as though attitudes are changing” within government.
A government spokesman said that tax-free shopping is available for all non-UK visitors “who purchase items in store and have them sent directly to their overseas address”.
It said: “Extending the scheme to EU nationals could cost British taxpayers around £1.4bn a year, meaning taxes would need to go up to pay for it at a time when we’ve already taken difficult decisions to get debt falling.”
Sales at Watches of Switzerland fell to £382m in the 13 weeks to July 30, down from £391m during the same period a year earlier.
However, the retailer said demand for luxury watches was continuing to outstrip supply, with waiting lists getting longer and average prices pushing higher.
