Yes, they should progress on completion of the NQT period if this has been extended either because they have completed it part-time or it has been extended for some other reason.
The pertinent information is contained in The Education (Induction Arrangements for School Teachers) (England) Regulations 2012 and in the School Teachers Pay and Conditions Document for the relevant year.
In the 2017 document, the pertinent sections were s 3.1(d), 19.2(c) and 3.4 - though these may have moved slightly in the 2018 document, I am not aware of any fundamental changes in these provisions with regard to this.
The school's pay and appraisal policies may be useful too.