The MRDF, a registered charity, had exclusively hired Legoland Windsor in Berkshire for more than 4,000 people on Sunday 9 March.
Over the last couple of weeks, the resort has received threats from far right organisations through phone calls, emails and its Facebook page, which had to be closed following a number of abusive posts.
Following discussions with police, Legoland and the MRDF decided to cancel the event.
A spokesman for Legoland Windsor said: "Due to unfortunate circumstances the private event scheduled for Sunday 9 March will no longer take place. This was an incredibly difficult decision made after discussions with the organisers and local Thames Valley Police, following the receipt of a number of threatening phone calls, emails and social media posts to the resort over the last couple of weeks.
"These alone have led us to conclude that we can no longer guarantee the happy fun family event which was envisaged, or the safety of our guests and employees on that day – which is always our number one priority.
"Sadly it is our belief that deliberate misinformation fuelled by a small group with a clear agenda was designed expressly to achieve this outcome. We are appalled at what has occurred, and at the fact that the real losers in this are the many families and children who were looking forward to an enjoyable day out at Legoland. We would like to apologise to them and to the organisers, and to thank them for their understanding. We hope that they will all be able to come to visit us during the season."
The last MRDF event of this type took place at Chessington World of Adventures.