His defection comes days after former shadow justice minister Robert Jenrick joined Reform.
It was facing a potential rebellion by some Labour MPs over how the law would apply to security services.
Sir Keir Starmer is due to respond to US President Donald Trump's latest move to take over the Danish territory.
An international trial involving 1,000 volunteers will aim to detect biomarkers associated with the condition.
The MPs says the UK "risks being left behind" if it does not adopt a ban similar to one in Australia.