Derbyshire, who was 49, passed away from the effects of a brain haemorrhage he suffered in 2014. He worked at Cook until 2011 as head of retail before leaving to join a family business.
An original target of £1,000 has now been almost doubled. Money raised will go towards Cleveland House, a care home that looked after Derbyshire when he fell into a coma.
In a statement, his family said: “The incredible support we have received as a family by every single member of the team involved with Cleveland House has been exceptional. Towards the end of Ian’s life they accommodated us all with open arms and comfort to the highest degree.
“In return for their fantastic work, we would like to help support any future families placed in similar difficult circumstances.”
A celebration of Derbyshire’s life will take place on January 5 at Landican Crematorium South Chapel, Birkenhead, at 12:30. The family have requested donations in place of flowers.
Chris Mottershead, Thomas Cook UK managing director paid tribute. He said: “On behalf of everyone who worked with Ian, we would like to express our heartfelt condolences to his family at this very sad time. Ian was hugely respected by his colleagues over the 11 years he worked with us, and his commitment and passion will be fondly remembered for many years to come.”