The letter, published in the Financial Times, says it is critical that roles such as chefs, bartenders and sommeliers be added to the shortage occupations list 'in order to save the industry under Brexit rules'.
It reads: "A huge number of individuals have left the industry and many operators simply cannot stay afloat with reduced staffing levels.
"Post-Covid customer demand is increasing, but now we don’t have the necessary trained staff."
It comes after the Government announced over the weekend that 5,000 HGV drivers will be able to come to the UK for 3 months in the run-up to Christmas, providing short-term relief for the haulage industry amid Britain's ongoing supply chain crisis.
A further 5,500 visas for poultry workers will also be made available for the same short period, to 'avoid any potential further pressures' on the food industry.
Trade body UKHospitality has previously estimated a shortfall of more than 200,000 workers across the sector.
A report published by the Office for National Statistics (ONS) earlier this month found that hospitality businesses are more than twice as likely as other industries to be experiencing challenges in filling job vacancies.
The Government does not include hospitality jobs on its shortage occupations list, which offers lower barriers of entry and reduced visa fees for certain professions.
Instead it has said the industry should train British staff, but business owners argue there is not the manpower in the UK to fill the vacant roles.
"Allowing the sector to recruit the staff it needs will result in higher turnover, more jobs and the resultant taxes returning to pre-pandemic levels more quickly," the letter says.
"Hospitality is not a low-pay sector, and these are skilled jobs paying skilled wages. The problem is not that we cannot compete with other sectors on pay, but that the staff are not there in the numbers required."
Other signatories include Pret A Manger co-founder Sinclair Beecham; chef Adam Byatt; Aquavit founder Wendy Haowei; and Richard Caring.
In a statement, the Home Office said: “We are closely monitoring labour supply and working with sector leaders to understand how we can best ease particular pinch points.”
“We want to see employers make long-term investments in the UK domestic workforce instead of relying on labour from abroad.”
