On Thursday, the pair said they submitted an offer of 115p a share for Lavendon. The joint bid comes after Lavendon's board rejected TVH's 111p offer in December.
Under the terms of the joint approach, London-listed Ashtead would acquire the British operations of Lavendon, while TVH, owned by parent company Thermote & Vanhalst, would take most of Lavendon's operations in Europe and the Middle East.
Ashtead and TVH pointed out in their joint statement that the approach is at a 45.6pc premium since December 2, the last business day prior to Lavendon entering into an offer period.
The bidders also made it clear they do not intend to make a higher offer unless the financial performance of Lavendon improves significantly.
Lavendon was quick to reject the latest approach, saying it was "opportunistic and significantly undervalues the company".