Over 50 crane drivers working for HTC Wolffkran unanimously rejected the offer at a mass meeting on Wednesday.
Now construction union bosses at Unite are threatening a full industrial action ballot in early summer, unless the company significantly improves its pay offer.
This could herald a summer of chaos on big construction sites, particularly in London.
Major projects where HTC Wolffkran is operating include: the regeneration of the BBC TV Centre at White City, the Westfield shopping centre in Shepherds Bush, the new Tottenham football stadium and the new Goldman Sachs HQ in Farringdon.
Unite’s acting national officer for construction Jerry Swain, said: “Workers are demanding an offer based on the company’s ability to pay.
“There is no way members will accept an offer which sees their standard of living effectively cut through rising inflation, when HTC’s coffers are bulging.
“If the company fail to significantly improve their pay offer then Unite members will not shy away from causing major industrial disruption, with high profile construction sites being targeted.”
In November 2014 workers at the predecessor company HTC Plant took strike action over a pay dispute and subsequently secured a greatly enhanced pay deal.