From what you have put, your order does not include "cohabitation with another man for a period in excess of 6 months". If this is not in the order it might be difficult to have SM written off but you might get variation. You need to weigh up the cost and risk of applying for variation as it can go up as well as down.
Co-habiting is a change in circumstance that can justify a variation. A court might not terminate the payments altogether, just in case the new relationship doesn''t work out and your ex and the children are left suffering undue hardship.
However, payments may be reduced to a nominal amount until the children reach independence and the term varied to end then too because your ex''s new relationship is settled.
A solicitor with knowledge and experience of how local courts view matters is in the best position to advise.