What drug was used in the itv version of The Big Four? The one that caused the paralysis in the two hostages and one of the murder victims.
By now, I have watched the relevant parts again, and although I think Vedran's answer is correct for the book version of the story, in the TV series, something different was used. I listened to it closely again, and understood something like Jasmine. There is a variety of Jasmine, the Yellow Jasmine, which seems to be very poisonous, containing Gelsemine. This poison is similar to Strychnine, it seems. The Wikipedia page on "The Big Four" seems to agree:
[...] orchestrates the entire Big Four setup, feeding the press with sensational clues and threatening letters and killing his victims to implicate the Peace Party members (whom he then kidnaps and drugs with immobilising gelsemine) [...]
I personally am wondering how Gelsemine can cause such paralysis, since it rather seems to produce convulsions. But that's fiction for you.
It was Belladonna:
Belladonna (also known as Deadly Nightshade, Devil’s Berries or Death Cherries) features in The Caribbean Mystery and The Big Four. Foliage and berries are toxic, containing a mixture of alkaloids including hyoscine (scopolamine) and atropine (both anti-cholinergic anti-muscurinic in action) and hyoscyamine (an isomer of atropine). Both the Emperor Augustus and Agrippina (wife and sister of Claudius) used belladonna to poison contemporaries. Symptoms include dilated pupils, blurred vision, tachycardia, dry mouth, slurred speech, urinary retention, confusion and hallucinations.
Source: Poisons Used In Agatha Christie
Although paralysis is not mentioned here, if you follow the first of the two links, you get:
Severe poisoning can cause paralysis, a coma and respiratory failure.