The rules state: "You can see friends and family you do not live with [or do not have a support bubble with] outdoors, in a group of no more than six. This limit of six includes children of any age."
And the rules also allow police to take action against and fine people who meet in larger groups.
One member of the public snapped the families on their phone and told the Mail they saw them "mingling" on several occasions.
Another visitor said, "They were clearly breaking Covid rules, in my opinion, because there were nine of them from two separate households. They were obviously all having a fun evening out. You could tell that the royal youngsters were having a great time.
"But I couldn't help thinking that it was one rule for them and another for the rest of us. It was really quite blatant."
Royal sources have said any contact was "inadvertent".
"The two families were given separate consecutive slots to visit the trail just before it opened to the general public. They arrived and departed in their own family groups.
"As anyone with young children will know, there were moments on the 90-minute walk where it was difficult to keep the two family groups apart, particularly at bottlenecks on the trail."
The Duke and Duchess of Cambridge and their children have been staying at Anmer Hall on the Sandringham estate for the past couple of weeks. They travelled there before Tier 3 and 4 rules were introduced, preventing non-essential travel from their home city of London.
The UK's Home Secretary Priti Patel said the rule of six means groups should not stop on the street to chat to other groups passing by.
"The rule of six is about making sure that people are being conscientious and not putting other people's health at risk," she said.
But some lawyers have said that interpretation is wrong, as the ban applies to gatherings "operated by a business, a charitable, benevolent or philanthropic institution or a public body".
