Britain is due to participate in electing candidates to the European parliament in elections set for May 2019, but Johnson suggested the country would be thinking about whether to send "a fresh batch of UK parliamentarians" to Brussels, indicating that Britain would have to kick off the two year period of negotiations after Article 50 is triggered before May 2017.
Read more: BoJo knocks sterling's mojo
"What we want to do is not do it by Christmas but obviously we can’t let the process drag on. If you think about it, you know, there’s obviously Euro elections coming down the track. I think people will be wondering whether we want to be sending a fresh batch of UK parliamentarians," said Johnson on the BBC's Andrew Marr show.
"UK Euro MPs to an institution that we are after all going to be leaving. So let’s get on it, we’re not going to let it drag on as the PM has rightly said, and I think we can be incredibly positive about [it]."
Johnson last week provoked the ire of Prime Minister Theresa May and sent sterling sliding after commenting that the formal process for Brexit would come early next year.
Former chancellor George Osborne late last week put in his two cents for a date for Article 50, telling an audience that May should wait until autumn while others have warned May to wait until after the domestic elections due to be held in France and Germany in the second half of next year.
On Friday, President of the European Parliament Martin Schulz echoed Johnson's thinking, warning that Britain should have left the EU by 2019 because it would be wrong for them to vote while negotiations were still taking place.