Mr Eastwood was speaking ahead of a meeting between the MacGabhann family and Chris Heaton-Harris on Wednesday.
He said the legislation would save lives in the North and should not be delayed due to the DUP’s Stormont boycott.
Said the Foyle MP: “Ahead of his meeting with the MacGabhann family tomorrow, I would urge the Secretary of State to do the right thing and announce that he will be taking forward this legislation at Westminster.
“Dáithí’s Law has the potential to save and change many lives by getting organ donations to those who need them.
“We have sadly seen tragic examples in recent weeks of children passing away while on the transplant list – that is what’s at stake here and we need to see recognition of that from Chris Heaton-Harris and his government.
“In my meetings with Dáithí and his family I have been struck by their positivity in the face of adversity and their determination to make a difference, not just for Dáithí, but those in need of organ donations everywhere.
“It sums up the problems at the heart of our politics that their fantastic initiative and inspirational campaign have been threatened by the dysfunction that so often holds us all back.
“We have seen repeatedly in recent years how the British government can interfere in our affairs when it suits them and they cannot shirk their responsibility when it comes to this legislation which would be a real force for good and make a positive difference for families across the North.
“We need to see this legislation taken forward at Westminster to give everyone in need of a transplant the best chance of survival.”