The Principal Place project consists of a 600,000 sq ft office element and a separate 50-storey resudential tower on Bishopsgate.

The rival builders are the last firms left in the final bidding stage for the huge office building, which ranks as one of the city’s biggest office projects.

A source told the Enquirer: “This is an interesting tussle. Skanska’s London building team has just won the Bevis Marks job in the city, but is keen to secure something big after Heron.

“McAlpine has got a Finsbury Square redevelopment but this is would be the big prize they want.”

Hammerson has detailed planning approvals for the offices as well as the more controversial 50-storey residential tower, which will be built under a separate contract worth up to £195m.

The residential project is scheduled to start in march 2013.