The firm now has its name on the hoardings at the regeneration scheme, which is east of the train station.
It is expected to take another year to complete Block B.
A source at HBG confirmed the move. The source said: "It came to a point where P&O and Balfour Beatty decided to go their separate ways. There was no loss of face on Balfour's side. There were certain issues that we were not party to that led to a parting of the ways."
A Balfour Beatty spokesperson said the firm had completed the first phase of the project, which consisted of enabling works, and had then ended its involvement.
She said: "It's fairly straightforward." A spokesperson for P&O said: "It was always the case that Balfour might or might not continue with the scheme. There was an agreement made that they would step down after phase one."
The move puts HBG in a dominant position in the scheme as it is overseeing the construction of four of the blocks, which amounts to £65-70m worth of work. HBG is building blocks C and D. Block A has yet to be submitted for detailed planning. The HBG source added: "The client has been very, very pleased with us so far on our work."
Balfour Beatty was first appointed for Block B in late 2002, beating off rivals including HBG, Carillion and Mowlem. The contracts included infrastructure works, landscaping, service engineering and the building of access roads.
Islington council gave the overall scheme – which is designed by architect RHWL – planning permission at the end of 2001. The structural engineer on the project is Cadogan Tietz.