The plan is for the protestors to imitate previous Brexiteer protests such as “Fishing for Leave” by sailing up the river to Parliament before it breaks up for recess.
Although the boat has a 180 capacity, the “No10Vigil Summer Boat Party” has only sold 84 tickets so far.
A message on their website reads: “We need to get 100 people onto this boat to make this a success.”
The prices for the party originally ranged from £22, for unwaged and students, to £50 for a VIP ticket.
But now there is a cheaper ticket of £10 available, and the website explains: “We need to fill the boat so have added this cheaper ticket option.
“Please donate what you feel you can. The most important thing is getting a good turn out.
“Any money over what we need to pay for boat expenses will be used to keep the #no10vigil going.”
The party will also include a Boris Johnson lookalike as well as “EU Super Girl” who is a singer and songwriter who took a gap year before going to university to try to overturn Brexit.
The event has been funded by crowdfunder and organisers claim they have raised enough to cover basic hire.
But they pledge that any leftover money will fund their “famous” “B***ocks to Brexit” stickers and leaflets.
The dress code is to bring or wear a flag.
They also claim they are sailing “to break Brexit before Brexit Britain”.
No10 Vigil is dedicated to trying to overturn the referendum result and describe it as “advisory”.
Their website states: “We believe that as further realities of Brexit materialise and further evidence that Brexit is bad for Britain comes to light, public opinion will continue to change.
“Ultimately the negotiation process will take far longer than we were led to believe, and if it doesn’t fall over with no deal, then what’s on the table will be much less attractive than staying in a reformed EU.
“There are also real risks that the United Kingdom will fragment.”