The TV news presenters have often clashed over the years, disagreeing over interviewing styles between Walker's role at BBC Breakfast and Morgan's former job fronting Good Morning Britain.
However, they both agreed that a photo showing the Queen sitting alone in St George's Chapel for Prince Philip's funeral was desperately sad, tweeting very similar sentiments about it.
Morgan wrote: "Has there ever been a more heart-breaking picture of The Queen? The cruel separation and loneliness suffered by so many in this pandemic, now endured by the world’s most famous woman as she says goodbye to her husband of 73 years. Just devastating."
Watch: Queen Elizabeth II lays to rest her 'strength and stay' Prince Philip
Walker, sharing the same photo, wrote: "This is such a poignant photograph. A reminder of how this pandemic has changed all our lives. The Queen sits alone, with a mask on, as she says farewell to her ‘strength & stay’ for so much of her life."
Although the presenters have often criticised each other on Twitter, Walker recently said following Morgan's departure from Good Morning Britain: "He likes to throw a few insults around, but underneath all the froth I think there is a decent bloke fighting to get out."
The Queen was joined by Prince Charles, William, Harry, Andrew, Edward and Princess Anne in a group of just 30 mourners paying their respects at the Duke of Edinburgh's funeral, with crowd limitations in place because of the coronavirus pandemic.
Harry attended the funeral after flying back to the UK alone, with his pregnant wife Meghan Markle remaining in the US on doctors' advice.
Morgan was recently ousted from Good Morning Britain for his comments about Markle following her tell-all Oprah Winfrey interview where she made a number of claims about her life with the royals.
Watch: Prince Philip and the Queen's marriage