The 61-year-old said he was "disgusted" by the BNP's use of a photograph of his grandfather to push its so-called Battle For Britain election campaign.
The leaflet, handed out to people across Britain, states: "Millions of our ancestors gave their lives to ensure you have the freedom to enjoy."
It then declares in capital letters "YOUR COUNTRY YOUR LAND YOUR HOME", before continuing "Do not betray their sacrifice!".
Mr Soames, MP for Mid Sussex, said: "I am outraged and appalled by the use of the picture by the BNP.
"They have no right to use my grandfather's name, who would have thought them a vile bunch.
"I am taking what steps I can and so is my family to see what can be done to prevent the name being used.
"I deplore the BNP action. It is a disgrace and I hope that anyone who looks at the adverts will find them repulsive."
Simon Darby, the deputy leader of the BNP, refused to amend the leaflet.
He said: "Mr Soames can sing and dance all he likes, we will not be removing Winston Churchill from our campaign.
"If Winston was around today he would be deemed a racist. He had some very strong views on immigration and if he was here today and had a choice of voting Tory or BNP I think he'd vote for us.
"I think he would be ashamed of the Tory party and would not be very happy with what has happened to this country.
"He would have more in common with the BNP than with the Tories, that's for sure."