In the circumstances described - No.
In Russell v. IRC  STC 195, Knox J held that only the original beneficiary can make a variation to which s.142 Inheritance Tax Act 1984 applies. This has been generally accepted.
Whilst s.142 (1) refers to the variation of “(a) any of the dipositions (whether effected by will, under the law relating to intestacy or otherwise) of the property comprised in his estate immediately before his death” “by an instrument in writing made by the persons or any of the persons who benefit or would benefit under the dispositions”, other than in argument before Knox J, there appears to have been no contention that “otherwise” should include a disposition by anther instrument of variation. The wording of the section does not refer specifically to a variation only being made by the person(s) entitled on death. However, mindful that Russell has been accepted as a correct statement of the law for some time now it would perhaps be a brave (and expensive?) move to challenge it.