However, a backer has been found "which allows the brand to restart".
The brand entered administration on 8 December.
A CAA spokesperson said Alpine Elements had "approximately 1,000" Atol-protected bookings at the time of its failure. He said: “This is a particularly sad day for customers and employees of Alpine Elements and we appreciate that those with bookings will be deeply concerned.
“However, the Atol scheme exists for exactly this kind of situation and we are making arrangements so that all Atol-protected customers can make a claim, whether they are due to travel or accepted refund credit notes for cancelled bookings.”
Managing director and founder James Hardiman said in a statement: "I am deeply sorry for this outcome, but it has been without question one of the hardest decisions I have had to make in 23 years of running my company.
"We have tried so hard, (for so long), to try and find a way through this, but the devastating effects of Covid, with its continued travel restrictions, lockdowns and – crucially for us – the lack of UK government support and guidance, have left us in an impossible situation.
"To this day, we are yet to receive refunds from the many suppliers to whom we paid in advance for the Covid-cancelled holidays of last winter season: such as airlines, accommodation providers, catering and other services.
"Without those refunds we have not had the available cash to refund our customers.
"Although we had a firm plan to pay back these monies – by Abta’s deadline of 30 January 2021 – the recent news that the ski season is unable to start means that I am forced into making this very difficult decision; one that my team and I have fought against for so long."
Hardiman said Alpine Elements guests’ holidays are "fully protected by Atol or Abta". Abta told TTG that Alpine Elements has not been a member since early November, however Hardiman clarified all customers remain bonded "and we have not taken any bookings without bonding in place". Abta added bookings made before 9 November remain Abta-protected.
Hardiman said the administrators would write to customers "very shortly" to advise them within 24 hours of how to make a refund claim.
Alpine Elements engaged an insolvency practitioner to help it try to find a buyer.
"We had serious interest from some very large organisations, but no substantial offers," said Hardiman.
"I was then faced with the awful reality of ‘no deal’ and the discontinuation of Alpine. In short, the complete loss of 23 years of work.
"We have since been working tirelessly to find investment and a buyer for the Alpine Elements brand.
"I can announce that very recently we succeeded in finding a backer which allows the brand to restart.
"Together with our investors, I am confident that with your support and understanding, we can bring the Alpine Elements brand and our unique and much-loved style back to you – to make our company stronger than before."
He continued: "I do understand that this process has been difficult and protracted for many of you, and I am so deeply sorry that it has come to this. I have put a lifetime of work into Alpine Elements and since starting in 1997 – with a one-chalet operation in Morzine – we have grown to become one of the largest Independent ski tour operators in the UK.
"It is thanks to the many thousands of loyal customers and our great staff – The Alpine Elements Family – that has made our company great.
"You have all helped me create such an exciting and well-loved brand; and your devotion, friendliness and spirit has helped me turn my passion for snow sports and sailing into a company where I can share my adventure.
"I know of no other way of life; and so, with a little time, I hope to bring Alpine Elements back to you, stronger than before."
Abta has posted information on its website about claims.