A challenge by a third man, whose case was rejected at the High Court on the same day as Mr Nicklinson's, will also be heard today.
The locked-in syndrome sufferer, who cannot be identified for legal reasons but is referred to as "Martin", suffered a massive stroke in August 2008.
He is unable to speak and virtually unable to move, describing his life as "undignified, distressing and intolerable", and wants to be allowed a "dignified suicide".
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Police found one child chained to the ground, another tied to a door with a dog lead, while six others were also rescued.
Wintry scenes across the UK this late in April have not been seen since the mid-1980s.
The Labour leader will also announce an inquiry into anti-semitism and other forms of racism to be chaired by Shami Chakrabarti.