I think that your problem is one of translation:
וכ"ז בתחלת יציאתו מביתו אבל כשהוא לן בדרך יוכל לומר תה"ד בבוקר כשמכין
עצמו לצאת אפילו כשהוא עדיין בעיר דכבר החזיק בדרך
And all this (what was said before) is at the start of his leaving from his house, but when he stays (sleeps over) along the way he can say tefilas haderech in the morning when he "arouses himself" to leave, even though he is still in the town (where he stayed over) because he has already established himself (literally strengthened) on the trip.
Thus, until one arrives home, it is considered that he is still traveling. In your example, once he leaves Manchester, every following day is considered part of the trip until he gets home. Leaving London (even to go home to Manchester) is not a separate trip.
When to Say Tefilas Haderech actually speaks about this.
- If one has in mind to stay overnight at a certain location when reciting Tefilas Haderech and after arriving and stopping at that
location he changes his mind and continues further or returns home, he
must repeat Tefilas Haderech.
שו"ע או"ח סימן ק"י סעיף ה'
As we see above traveling home is considered part of the trip.