Jacob Rees-Mogg and his young son were heckled by Brexit protesters in Westminster as they leave Parliament.
The demonstrators could be heard shouting "shame" as Mr Rees-Mogg and his son passed the protesters on Millbank.
Similarly, boos and shouts of "shame on you" were directed at Mrs Leadsom as she walked up the street surrounded by officers.
Hundreds of thousands of protesters gathered in London today to call for a second vote on Brexit, as MPs approved an amendment which saw a vote on the Government's deal pushed back to next week.
Later, Mrs Leadsom tweeted: "Thank goodness for our superb police. Just walked home safely from HoC with their protection – why do the so called 'People's Vote' protesters think it's ok to abuse, intimidate and scream in the face of someone they don't agree with?
"So frightening, and so grateful to the police," she added.
Labour's Diane Abbott was also filmed being targeted by pro-Brexit demonstrators who asked if she was wearing "Jeremy Corbyn's slippers" and told her "it's about time we stopped all this".