Just had a quick look at the research briefings posted by time4chocolate (on page 36 of this thread) - which refer to the Immigration Act 2014:
www.legislation.gov.uk/ukpga/2014/22/section/66/enacted
Deprivation if conduct seriously prejudicial to vital interests of the UK
(1) In section 40 of the British Nationality Act 1981 (deprivation of citizenship), after subsection (4) insert—
“(4A) But that does not prevent the Secretary of State from making an order under subsection (2) to deprive a person of a citizenship status if—
(a) the citizenship status results from the person’s naturalisation
(b)the Secretary of State is satisfied that the deprivation is conducive to the public good because the person, while having that citizenship status, has conducted him or herself in a manner which is seriously prejudicial to the vital interests of the United Kingdom, any of the Islands, or any British overseas territory, and
(c) the Secretary of State has reasonable grounds for believing that the person is able, under the law of a country or territory outside the United Kingdom, to become a national of such a country or territory
(2)In deciding whether to make an order under subsection (2) of section 40 of the British Nationality Act 1981 in a case which falls within subsection (4A) of that Act ,the Secretary of State may take account of the manner in which a person conducted him or herself before this section came into force.