Conservative MP Richard Shepherd said the Court had expanded its reach into the "nitty gritty" of domestic law and there seemed to be "no trigger" for UK courts to assert their own supremacy.
"This is now, to many people, intolerable," he said.
Government divisions over human rights legislation came to the surface in September when Mr Clarke criticised Cabinet colleague Mrs May after she said a man who avoided deportation on the grounds that his family life should be protected had cited his ownership of a pet cat.
Lord Phillips of Worth Matravers, the President of the Supreme Court who was also giving evidence, was asked whether UK judges were giving too much consideration to the right to familiy life in deportation cases compared with public interest factors.
"I don't think we are setting out to do that. It has happened in one or two cases," he said.
"Sometimes you get a case of extreme facts which produces a very understandable result. Then people try on feed on this as setting a principle or a precedent. The answer is they should not."
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