Royal warrants are determined by the Queen and Prince of Wales and the latter has pledged his support for the campaign against the factory's closure.
Labour MP for Rhondda Chris Bryant is now demanding that the system for awarding royal warrants be reviewed.
He said: 'The criteria by which they [royal warrants] are awarded is not subject to any parliamentary scrutiny. I am writing to the Lord Chancellor to review how they are granted and in particular, whether they should continue for companies that outsource abroad.'
Bryant wants to see Burberry stripped of its status if it closes the plant in Trecorchy.
Oscar-winning actress Emma Thompson has also joined the long list of public figures to condemn the clothing company.
Thompson said the brand would be 'inauthentic' and 'bastardised' if made in Chinese factories. She called the company 'greedy and unethical'.
Her plea follows a campaign by numerous celebrities, the Church of England - which owns£2.5million worth of Burberry shares - and royalty, against the factory closure.
Thompson added: 'When I buy clothes, I always check to see where they are made. When an item that is so clearly branded as British to the core is made in China, I'm afraid that I often put that article straight back, suspecting corporate greed and unacceptably low wage packets. Burberry should not make this move.'
Other celebrity protesters include Hollywood actors Ioan Gruffudd and Rhys Ifans, opera singer Bryn Terfel, Charlotte Church and comedian Max Boyce.
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