The photo was taken by US tourist Staci Martin as she posed with the officer 45 minutes before he was stabbed by Khalid Masood outside Parliament.
It has emerged Masood, 52, was born Adrian Elms in Dartford, Kent. It is said he used a number of aliases and was known to police.
PC Palmer, 48, was one of four victims killed on Wednesday.
Masood drove into pedestrians on Westminster Bridge before crashing his car into railings and then running into the grounds of Parliament, armed with a knife. He was shot dead by police.
Aysha Frade, a teacher in her 40s, and US tourist Kurt Cochran, 54, were killed on Wednesday, while a 75-year-old man died on Thursday evening after his life support machine was turned off.
Three women and five men have been arrested in London and Birmingham on suspicion of preparation of terrorist acts.