The group of campaigners and staff from the charity Age UK gathered outside Number 10, holding signs featuring slogans including "TV is our lifeline".
They posed for pictures in front of the door before handing over the petition, which has so far received some 620,000 signatures.
The petition on the Age UK website, entitled Switched Off: Save free TV for older people, demands "the Government takes back responsibility for funding free TV licences".
Funding the free licences is due to be transferred from the Government to the BBC next year as part of an agreement hammered out in 2015.
The BBC has said funding the universal scheme would mean the closure of BBC Two, BBC Four, the BBC News Channel, the BBC Scotland channel, Radio 5 Live, and several local radio stations.
Age UK charity director Caroline Abrahams said: "Today we presented Age UK's #Switched Off petition to Number 10, backed by 634,334 people who are telling the Government to save free TV licences for over-75s.
"Free television when you're older is more than just a box in the corner of the room - it's a lifeline for millions, especially those who are living alone and with health problems or disability.
"We presented our new Prime Minister with just a taster of how older people feel about this. Older people have told us, even begged us to speak out on their behalf and fight their corner.
"We call on our new Prime Minister to listen to the staggering number of people of all ages who truly believe the funding of TV licences firmly rests with the Government and not the BBC. We ask him to intervene and abide by the last Conservative manifesto pledge to keep free TV licences for the over-75s."
Age UK last month organised to have some 37,000 letters delivered to the Tory Party's Westminster headquarters, urging then-leadership hopefuls Mr Johnson and Jeremy Hunt to reverse the move.