Thanks TerrePorter, I am not sure if that is what I needed.

I ended up with a resolution though, and I think it's bit of a hack and would welcome any suggestions on something cleaner.

I have extended my original Pupil model and created

<?php

class PupilWithSchoolIdentifier extends Pupil {

    protected $primaryKey = 'txtSchoolID';

}

I then use this model in my Set model

<?php

class Set extends \RHS\Eloquent\Model {

    protected $table = 'TblTeachingManagerSets';

    protected $primaryKey = 'TblTeachingManagerSetsID';

    protected $accessibleColumns = [
        'TblTeachingManagerSetsID',
        'intSubject',
        'intYear',
        'txtName',
        'txtTeacher',
    ];

    public function pupils()
    {
        return $this->belongsToMany('PupilWithSchoolIdentifier', 'TblTeachingManagerSetLists', 'intSetID', 'txtSchoolID');
    }


}

I have found the code that I want to adjust in the BelongsToMany class in Laravel.

protected function setJoin($query = null)
	{
		$query = $query ?: $this->query;

		// We need to join to the intermediate table on the related model's primary
		// key column with the intermediate table's foreign key for the related
		// model instance. Then we can set the "where" for the parent models.
		$baseTable = $this->related->getTable();

		$key = $baseTable.'.'.$this->related->getKeyName();

		$query->join($this->table, $key, '=', $this->getOtherKey());

		return $this;
	}

However this seems to always want to use the getKeyName method on the model, which returns the primary key. Perhaps it would be good to allow passing a parameter through so that the pivot foreign key can be specified/overridden?

As I say, what I have done works, but it feels a little dirty, I am sure there is a better way.