The £598,000 RHS-funded building, which is scheduled for completion next spring, will provide the charity with a state-of-the-art facility in which to carry out scientific investigations of plant diseases and pests.
RHS head of science Roger Williams said: "This will be the first facility of its kind dedicated to advancing the science of gardening.
We are very grateful to those who have already helped us financially.
"We still have more fundraising to do but we are confident that we will get the funds to complete this important project."
Each year, through plant samples sent to the RHS advisory department, the charity's scientists discover five or six diseases and pests that are new to the UK.
The new facility will improve the ability of the RHS to study these pests and diseases and develop advice on control measures.
The RHS aims to increase awareness and understanding of the importance of science to gardening.
In partnership with polytunnel company Unigro, the facility will be equipped with heat exchange technology, including a swimming pool-sized tank underneath the building that will enable waste heat built up during the day to be recycled for warming at night.
The new building will also have solar panel cells to generate electricity and the capability to recycle unused energy as stored heat.