That's generally possible. You may use your inbound journey from any foreign country or port or airport. 

But:

You'd need a 5th travel day for this journey as you already did use all of your 4 travel days (you did write that you are holding a 4 day Global pass).

Remember: On two of your travel days you may also use your pass in your homecountry (outbound / inbound). These are no additional travel days.

By the way: The Eurostar train from London is also part of your outbound journey. But that's possible to do because it's on the same day.

Summary: If you are holding a 4 day Global pass and this is your fixed itinerary it's not possible to do. But you may buy a normal ticket for the cheapest part of your trip (should be Wien to Budapest).

I count only 4 days: 16, 18, 20, 22 September.

And London to Wellingborough on September 30th.

Oops, missed that one.

You could also buy a normal ticket for Vienna-Budapest. They seem to start at €13 via MÁV.

Be aware that the night train Paris - Vienna doesn't run daily. It won't run on 18th September so you'll need to travel on 17th or 19th September or by daytime train

Thank you for your help, it’s clear to me now