If the payout from the MIG insurers to the Halifax occurred more than 6 years ago then current opinion would suggest that this part of the shortfall claim is a simple debt and as such is now statute barred, unless you have acknowledged the debt in any way (see yesterday's new answers).(posted 7969 days ago)Somewhere in the dossier you have received there should be correspondence with the insurer in some form (not necessarily letterheaded paper) indicating the insurer's acceptance of the MIG claim and a record of the payment being received by the Halifax with a date.
Under subrogation rights a lender is allowed to pursue MIG payouts on behalf of the insurer, but unless your mortgage deed and conditions specifically make this a specialty debt I still think that it is a simple one since it arises out of an insurance contract. See recent postings on upcoming court cases etc. and the 6/12 year Limitations Act.