The harrowing tale set in a psychiatric day centre, in which Poppy was played by 'Pirates of the Caribbean' actress Naomie Harris, was watched by a 6% share at 9pm.
Channel 4 will be pleased with the audience, considering the drama's melancholic tone and oppressive material.
It was well received by TV critics, with The Times' Andrew Billen describing the two-hour film as "touching" and . Including Channel 4+1, 'Poppy Shakespeare' drew 1.4m viewers and a 6.3% share.
Earlier in the evening, a Channel 4 'Dispatches' documentary on life in Tibet under Chinese occupation, 'Undercover in Tibet', brought in 700,000 viewers with a 2.9% share at 8pm-9pm. Including Channel 4+1's ratings, the audience rose to 800,000 and a 3.1% share.
The final part of ITV1 drama 'The Fixer' bowed out with the lowest audience of its three-part series, with 4.5m viewers and a 19.5% share at 9pm.
The 9pm slot was won by BBC One's 'Crimewatch' with 5.5m viewers and a 24% share.
In the multichannel youth battle, 'Skins' netted E4 an impressive 700,000 viewers and a 4% share of multichannel viewers at 10pm, but 'Dis/Connected', BBC Three's attempt at aping the popular teen drama, fell flat.
BBC Three's new drama 'Dis/Connected' was watched by only 72,000 viewers and a 1.3% share of multichannel viewers at 11.45pm.
BBC Three is to bring back its chatshow 'Lily Allen and Friends' for a second series. The show has had a cool reception from critics but after opening with 255,000 viewers in February has averaged around 300,000 over recent weeks.
Danny Cohen, the channel controller, said: " Lily is a star. She has developed astoundingly well as a TV host in just a few weeks and has established herself as a firm favourite with the young audiences BBC Three targets."