Zac Goldsmith, MP for Richmond Park and North Kingston, will join representatives from Prospect, PCS and GMB to hand in the 100,000 signature petition.
Goldsmith, whose constituency is home to Kew Gardens, said: "It’s not clear to me that Kew Gardens can sustain its extraordinary work with the level of cuts being imposed.
"Kew Gardens is a national jewel, and it would be a tragedy if its work and reputation were to suffer as a result of excessive cuts."
Prospect negotiator Julie Flanagan said: "Successive independent reviews of Kew have praised the quality and value of its scientific work and recommended that its public funding be maintained or increased.
"Kew has already lost approximately 50 posts, vacancies are not being filled and management is planning the loss of a further 50-70 posts.
"Cutting staff reduces Kew’s capacity to fulfil its statutory obligations, to carry out its leading science and conservation, and to generate its own revenue.
"It has been heartening to see how much people from across the globe recognise and support Kew’s value. It’s a tragedy that the coalition government can’t do the same."
Kew announced a £5m deficit for the year and plans to axe about 125 science and public engagement staff in March 2014.
Defra secretary of state Owen Paterson has ruled out an emergency bail-out.