Mr Justice Tugendhat will give his decision on the meaning of an allegedly libellous tweet she sent after a Newsnight report that wrongly implicated the Tory peer in child sex abuse allegations.
Earlier this month the judge reserved his decision in the case.
If the judgment goes in Lord McAlpine's favour, there will be another hearing at a later date on the appropriate level of damages, unless the two sides reach a settlement.
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David Cameron has begun a whirlwind tour of Europe to discuss his terms for renegotiating the UK's membership of the EU with key leaders.
Through the rest of today showers will continue across many northern areas, whereas for much of England and Wales it'll stay largely dry.