The announcement puts an end to the major proposed US$775m merger, which the two companies entered into an agreement for in August 2021.
Canada-based Ritchie Bros says its decision follows the referral of the proposed acquisition to a Phase 2 review by the UK Competition and Markets Authority (CMA).
It added in a statement: "Amongst other things, completion of the agreement is conditional on receipt of clearance from the CMA on terms satisfactory to the RB Purchaser, but after extensive consideration the RB Purchaser does not believe there is any realistic prospect for approval by the CMA on such terms given the significant concerns raised by the CMA to date."
Ritchie Bros CEO Ann Fandozzi said the company was disappointed by the decision taken by the CMA to refer the proposed acquisition to a Phase 2 review and respectfully disagrees with their views.
She added: "While we believe the proposed acquisition would have accelerated our strategy, we remain committed to forging ahead in our transformational journey to become the trusted global marketplace for insights, services and transaction solutions. We will continue to seek out and execute on organic investments and key acquisitions to accelerate our pace in achieving our ultimate vision."