The calls follow the discovery that many toys on popular online marketplaces are counterfeits of reputable products.
Some also contain dangerous miniature magnets, restricted chemical ingredients or exposed button cell batteries.
A toy safety investigation by The British Toy and Hobby Association found that, of a random sample of toys from online retailers, 88% were found to be illegal and 48% unsafe for a child to play with.
Sir Greg said: “There are growing concerns from both within the toy industry and amongst MPs, that the safety of toys sold through online marketplaces is insufficiently regulated.
“These are shocking figures and underscore the need for action.
“I am pleased that the Office for Product Safety and Standards is conducting a review of the UK’s product safety framework, but the Government should also investigate this issue to see if further action is required.
“As we approach the Christmas period, it is also important for parents to be aware of how many unsafe toys are being sold through the internet.
“I encourage everyone in East Yorkshire to be vigilant, particularly when purchasing presents online.
“If in doubt, visit a reputable local shop where good quality toys can be purchased.”