The seven new schools will be located in Newham, Lambeth, Barnet, Waltham Forest, Greenwich, Bromley and Camden.
The first estimated build cost has come in ahead of initial expectation for the London batch which had been estimated at around £50m.
London batch
• Stratford School Academy (Secondary)
• Lansdowne School (Special)
• Hawkswood (Pupil Referral unit)
• Harris Academy Greenwich (Secondary)
• Harris Academy Bromley (Secondary)
• Pardes House School (Primary)
• Maria Fidelis School (Secondary)
Work will now progress to the planning application stage.
It is BAM’s second batch after being appointed to deliver the £27m set of four schools in the Midlands last month.
Bam is also in the last two bidders for last two of the four remaining batches of schools under the Government publicly funded programme.
Both are in the North West region, worth an estimated £42m and £25m.
School bidders table
South: Bidders Kier and Interserve
London: Winner: Bam Construct, £75m
East: Bidders Kier and Wates
Midlands 1: Winner Wates, £36m
Midlands 2: Winner Bam Construct, £27m
North East: Winner Sir Robert McAlpine, £64m
North West 1: Bidders Bam Construct and Carillion
North West 2: Bidders Bam Construct and Willmott Dixon