to turn/ tighten the screw [on]

[Theseus]

To turn or tighten the screw [on] is slang and means to increase the pressure which is already on a person, for example by using threats, in order to force them to do a particular thing.
--Parisian taxi drivers are threatening to mount a blockade to turn the screw on the government.

 

[Hellegennes]

I can think of the following, which I think is roughly equivalent but not slang:
Αυξάνω τις πιέσεις

There are also two other phrases, which are used on slightly different occasions; namely:
Σφίγγω τον κλοιό (it implies a literal or metaphorical war against someone but sometimes it's equivalent to "to tighten the screw")
Βάζω το μαχαίρι στον λαιμό κάποιου (to give no choice to someone -put initial pressure)

 

[AoratiMelani]

Μια που το πιάσαμε, θεωρείτε ότι η μετάφραση "Το στρίψιμο της βίδας" είναι η πλέον κατάλληλη για τον τίτλο του έργου "The turning of the screw" του Henry James;

Εντάξει τώρα έχει ήδη κυκλοφορήσει έτσι, αλλά το θέτω χάριν συζητήσεως (εξάλλου πάντα μπορεί να γίνει μια άλλη μετάφραση).

 

[Zazula]

I can think of the following, which I think is roughly equivalent but not slang:
Αυξάνω τις πιέσεις

Even less slang:
Κλιμακώνω τις πιέσεις

 

[drsiebenmal]

The turn of the screw (καμία σχέση με το The Taming of the Shrew :))