The lobbying campaign is being led by the British in Europe group, which was formed after Brexit to fight to protect the rights of British citizens living in the EU after Brexit.
Essentially the campaigners want to get Members of the European Parliament (MEPs) on their side as negotiations between the EU and the UK reach a critical stage.
In December the European Commission will decide whether it deems "sufficient progress" has been made in "Phase One" of the talks, which will have covered future citizens' rights.
If it decides that is the case, then the commission will allow negotiations to move on to stage two, which will cover a future trade agreements between Britain and the bloc.
But campaigners fear that if talks move on "there is a risk of a political stitch-up" in that the issue of citizens' rights will be swept under the carpet as trade talks take prominence.
"It’s more vital than ever that the European Parliament holds the line over the next three weeks," says the British in Europe group.
"We urgently need to recruit MEPs across the EU27 as our allies, which means we need to help them to understand what’s at stake and the very real risks we face of losing rights that are essential to our ability to "live our lives as before".
"On 20 November the British in Europe steering team wrote to every MEP – 751 of them! – setting out the issues; now it’s time for everyone to do the same."
Kalba Meadows who runs the Remain in France Together (RIFT) campaign told members: "I can't stress to you enough that this will be the most important lobbying campaign that we have ever, and possibly will ever, run."
"There are serious political manoeuvrings going on at the moment to get the European Commission to recommend a decision of 'sufficient progress' in December so that trade talks can begin - and yet our citizens' rights are NOT yet fully protected and we are at risk of being sold down the river."