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The move came almost a year to the day since Francois Barrault, the division's former boss, appointed Hoggarth.
BT has blamed Global Services, which supplies outsourced network and software development, for a £1.6bn write-off in the value of its contracts, dragging down its results.
Barrault left in November with a golden handshake of £1.6m as BT shares slid 30%.
BT supplies the Spine, a national private network that is at the heart of the NHS's vast £12.4bn plan to revamp the health service's IT, but the loss-making contracts are believed to refer to work that BT picked up when Fujitsu pulled out of contracts to supply electronic patient record systems.
However, BT clawed back £500m of £1.2bn losses in renegotiations with the NHS.
A BT spokesman said more than 80% of the Global Services executive team had left. "We've reduced total labour resource in GS by close to 5,000 in Q4 and Q1," he said.
The division was also doing more regular contract reviews to assess their commercial and financial risks. It had also cut what it pays its contractors by up to 35%, he added.
Global Services cut its capital expenditure by 47% in the first quarter by buying better and meeting tougher investment return criteria. Operating cash outflow was £178m better as a result, the spokesman said.