May is planning to live in the house for a few days once built.
It will be a full-sized property complete with staircase, toilet and shower.
Three million bricks have been delivered to the site – but May is appealing for more donations.
"If people do have bricks that aren’t being used that they would be happy to donate to a very worthy pioneering Lego cause, then we’ll be happy to take them off your hands," he told the BBC.
Anyone interested in taking part in the Lego house build, or who has Lego bricks to donate, should e-mail firstname.lastname@example.org.
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