Mr Woodcock said while Banbury folk followed the lockdown restrictions and, in some cases, lost loved ones without being able to say goodbye, politicians were wilfully breaking the rules.
Mrs Prentis said she understood people's anger and was pleased the Prime Minister had apologised and promised an inquiry.
Mr Woodcock said: "In 2020, 139 people in Cherwell died from Covid. Countless more lost loved ones. We missed special moments, gave up on a family Christmas and in many cases lost the chance to say goodbye. The people of Cherwell followed the rules.
"Now it is clear that not only did Boris Johnson’s Downing Street fail to follow the rules, they laughed about it and then they lied about it. They are laughing at every single person in Cherwell who did their best to help our community get past this terrible virus. And now they are lying to our faces.
"Again and again and again with this government, they let us down and then they lie – and now we know they are laughing at us behind the scenes. It’s one rule for them, another for everyone else.
"How can our Member of Parliament, Victoria Prentis, look the people she represents in the eye, and suggest any different?"
Mrs Prentis said in response: "The last 22 months have been really challenging for all of us, especially for those who have lost loved ones to this awful disease.
"In this context, I completely understand how angry many people are about the events which appear to have taken place in Downing Street last December. I am pleased that the PM has apologised and has asked the Cabinet Secretary to hold an inquiry.
"I know that most of us made real sacrifices to keep to the restrictions which were put in place to keep us safe. I’m so sorry for the hurt that this issue has caused to those who have tried so hard during the dark days of this pandemic."