A statement on the petition said: “NHS staff spend days such as Christmas and New Year with complete strangers, with their patients and colleagues, helping to save lives.
“For doing this they get a little bit more money, but the job they do is priceless.”
GSST Unite are also threatening strike action if the proposal is not reversed.
Last year thousands of London NHS workers today went on strike over low pay rates.
A spokesman for Guy's and St Thomas' NHS Foundation Trust said: "The organisers of a proposed demonstration regarding national pay issues on April 30 have publicised St Thomas’ Hospital’s main entrance as the assembly point.
"Access to the main entrance to St Thomas’ Hospital for patients, visitors, and staff will be maintained at all times. Patient care will not be affected."