During an inquest into the death earlier this year the Oxleas NHS Foundation Trust, which oversees Green Parks House, said Mrs Mager's death "could not have been predicted or prevented".
But after court proceedings were served, the Trust admitted liability, saying they should have prevented her death.
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The new design is inspired by Westminster Cathedral.
Just 200 yards from Harrods, the one bedroom flat is significantly lower than the current market rate for the prestigious area.
A documentary on the career of the late London singer Amy Winehouse will be broadcast live this evening at half six.