One of the paintings was the one in the image above, a 1954 portrait by Graham Vivian Sutherland (1903-1980), his Wikipedia entry here. This portrait was noteworthy because Churchill and his wife hated it, and as explained here, Clementine had it destroyed after Winston's death. She did the right thing.
Even though the painting is gone, traces of it remain in the form of sketches and studies Sutherland made. Some of these can be found by Googling. There is one study that can be viewed in person if you happen to be in London.
Here is my photo of it taken at the National Portrait Gallery in April. Click to enlarge, and you might be able to read the plaque dealing with it. Better yet, you can find a larger image by linking here to the Portrait Gallery's page dealing with the painting. The caption material can be found by scrolling down.
Although Sutherland seems to have been highly regarded in Britain in his day, his work is not to my taste. Images of many of his painting can be found on the Internet, but I include a few below so that you can get a sense of what he was doing during his career.
During the 1930s and 1940s he favored Surrealistic and semi-abstract styles.
He made a number of Christian-themes paintings and created works for the Coventry Cathedral replacement.
A portrait painted a few years before the Churchill project. Also anti-flattering.
Made when in his mid-70s.