By Car and Ferry
Car
Option 1. Drive to Hull and take the overnight P&O ferry to Rotterdam or Zeebrugge. The shortest route is via Rotterdam, providing a leisurely drive across Holland to arrive in Rinteln by mid-afternoon.
Option 2. Drive to Newcastle and take the overnight DFDS ferry to Amsterdam. Then a leisurely drive across Holland to arrive in Rinteln by mid-afternoon.
Option 3. Drive to Dover or Folkstone for the short ferry or Eurotunnel crossing to France. Then drive a choice of routes to Rinteln. This is a long journey, and would be ideal if you wanted to break the journey on the way for some sightseeing.
By Plane and Train
Plane
There are several possibilities, and they are regularly changing with airlines bringing in new routes and discontinuing others. Below are two possibilities.
The demise of Flybe has reduced the options for flying to Germany. Alternatives from Manchester are to Düsseldorf (Eurowings) or to Cologne or Berlin (Ryanair).
There are frequent trains to Rinteln from both airports, but Düsseldorf is the most convenient with fewer changes. Train times and tickets can be found on Trainline.
A good way to travel is as a foot passenger on the ferry to Amsterdam then to Rinteln by train.