Branches in Mengham, West Town, Havant, Alresford, Drayton and Cowplain will be shutting.
Customers paid tribute to the bakery and stressed their sorrow on Facebook.
Lesley Wenden said: ‘Very sad news. Heidi's supported the Lifehouse Soup Kitchen for many years by supplying wonderful cakes and bread.’
‘Thank you is not enough for the joy of biting into one of your cakes.’
The highly sought after baked goods will be missed by many.
Dave Leggett said: ‘I need to pre order a year's worth of cheese straws.’
Andrew Mendel added: ‘That's sad, I loved their custard slices, I always bought them.’
Some residents had a greater connection to the business beyond the cheese straws.
James Justin Taylor said: ‘Such a shame, I had the pleasure to meet Heidi’s dad just before his passing.
‘He was so proud of her and how the business was going, this is truly heart breaking.’
Karen Palmer added: ‘I loved working at Heidi's, what a shame.’
Owner Heidi Elliott said the reason behind the downsizing plans was that it was not financially viable for them to continue.
Heidi’s will close its Alresford patisserie at the end of September when the lease on the shop building expires.
Shops in Hayling, Drayton, Cowplain and Havant will shut in December.
The company plans to refurbish its Emsworth store – reopening its bakery operation early next year.