On 11 September, MPs will vote on assisted suicide for the first time in 20 years. If enacted, the bill would give dying people the right to end their lives.
The campaign, which is backed by Patrick Stewart, aims to fund at least 10 billboards in key locations across the capital to spark debate in the weeks leading up to the vote and to put pressure on MPs.
A spokesperson for Dignity In Dying told Huffington Post UK that assisted dying is "supported by an overwhelming majority of the public", and that this must be acknowledged when the issue is debated in the House of Commons.
So far, the Crowdfunder has raised over half of the £10,000 target, with the first £3,000 being raised within three hours of the campaign launching.
"Terminally ill people should not have to suffer against their wishes, and everyone has a stake in this debate as it is something that will affect all of us when the time comes, and most people want choice at the end of life."
“As part of the campaign our supporters are generously contributing to a fund that will get this message seen as widely as possible, and we expect everyone across the UK to engage in the case for change," said Dignity In Dying.
"We’ve already raised half of our target in less than 24 hours, and this shows that assisted dying is a crucial social issue that people care deeply about.
"With one Briton travelling to Dignitas every fortnight, and over 300 terminally ill people taking their own lives at home behind closed doors in this country, it is time that Parliamentarians realise they can no longer accept the current situation and must act to end people’s suffering.”
Celebrities including Terry Pratchett, Jo Brand and Hugh Grant have previously spoken out about the "broken" assisted dying laws in the UK.
Phil Geraghty, Managing Director of Crowdfunder, told Huffington Post UK: "We believe in the power of crowdfunding not only to give organisations the opportunity to raise funds, but also as a way for the public to have a voice.
"This is what Dignity In Dying are doing with their billboard campaign, by enabling the public to fund the project, they are creating a social movement.
"Having raised over 50% in less than 24 hours shows the support that is out there and the appetite from those wishing to see a change in the law."