The upmarket fashion retailer plans to relocate production overseas, with a loss of more than 300 jobs.
Welsh rock band The Automatic, TV presenter Steve Jones and singer Tom Jones have also voiced their concerns about the plant's closure, which is scheduled for the end of March.
Tom Jones said: 'As a local boy, I know how important this factory has been to the community in the Rhondda. I therefore urge the Burberry management to withdraw their plans to close the Treorchy factory.'
The GMB Union is intensifying its campaign over the next month and is planning to hold demonstrations outside Burberry's flagship stores in London next Saturday. The union is also co-ordinating simultaneous international protests outside Burberry's flagship stores in New York, Paris and Rome in early February.
Rhondda MP Chris Bryant is calling for Burberry to be stripped of its Royal Warrant and is debating the issue in Parliament today.
Bryant said: 'A Royal Warrant is our national seal of approval and it should only go to great British companies that stand by traditional British values.'
Other celebrity protesters include Hollywood actors Ioan Gruffudd and Rhys Ifans, Oscar-winning actress Emma Thompson, opera singer Bryn Terfel, Charlotte Church and comedian Max Boyce.
Burberry's executives will go before the House of Commons Welsh Affairs Select Committee at the end of next month to explain why they are closing the factory.
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