Ferry from England to Amsterdam

Here's a starter:

It's probably going to be either Stena or DFDS.

The Amsterdam ferry port is out to the northwest about fifteen miles at Imjuiden.

To leave from Newcastle, you'd have to go way north from Shropshire.

I think the Harwich ferry goes into the Hook of Holland which is about twenty miles northwest of Rotterdam.

There's probably a million better ways to make the trip.

This will be a pretty long, multi-stage trip. Ferries from Harwich to Hook of Holland are either first thing in the morning or overnight. My personal suggestion would be to fly to Schiphol from Birmingham Airport - either FlyBe or KLM. You can get a train from Shrewsbury to Birmingham New Street and then to Birmingham International railway station for the airport.

Philips answer would be the quickest route definitely but I wanted to add more info on ground-side routes, in case there is a reason you've not mentioned flying in your original post (phobia, medical condition or just addicted to the romance of train travel :)
First, forget the routes from Newcastle to Amsterdam or Hull to europoort. Both routes sail down the east coast far slower than a coach or train covers the distance south; they're mainly for container trucks which have restrictions to speed and driving time on the motorways.
As I drive over, the Harwich ferry is my first choice as driving down to Calais and back up to Amsterdam adds a lot of time & fuel cost. However since Stena took the catamaran off of the route there's only the 7-hour ferries, daytime and overnight, and the ferries now on the route are quite poky compared to the mini-cruise-liners that ran the route decades ago (1/2-deck of passenger services compared to 2) - again, the service is mostly geared towards container trucks. The overnight gets in quite early but trains are running into Rotterdam Centraal and trains from there to Amsterdam are frequent and fast. A cabin is mandatory for the overnight though - they are surprisingly comfortable but it adds to the cost.
An alternative which, as foot passengers, is a lot cheaper than you might imagine yet is fast and comfortable, is the Eurostar; they offer a through-ticket from London to Amsterdam (e.g. at the moment there's a £99 return offer). You'd need to take the train down to Euston from Birmingham, tube over to St Pancras, take the Eurostar to Brussels where you change onto a high-speed Thalys to Amsterdam. The trip from London takes about 5 hours, allow 2.5-3 hours to get down from Birmingham and over to St Pancras. Not nearly as fast as the plane (about 1.5hrs not including check in and waiting around for baggage) but not terrible and if you book the trains well ahead, not stupidly expensive. You get to see some nice countryside on the way too.
One more possibility. If you aren't too tall (legroom) and can take a long coach trip, have a look at Eurolines. You can go Birmingham to Amsterdam with 1 change at Victoria for less than £50 single. The coach goes over at Dover so it's either 1 very long day, or an afternoon and overnight. If you can sleep OK on coaches, it's another option to have handy... Never taken it myself though - only Norwegian coaches have enough legroom for me - so I can't tell you what it's like from experience. The Site has plenty of info though.

Good advice from the above, especially Aiken for the comprehensive reply.

Just a couple of things - there are two train companies which serve the route Shrewsbury to Birmingham International. The London Midland trains, which originate at Shrewsbury, go no further that Birmingham New Street at which point you would need to change to one of the other frequent trains to the airport (check your train ticket for restrictions). The Arriva Wales trains, which come from further west, in Wales, run all the way through to the airport, stopping in Birmingham New Street but you stay on and go the one further stop.

I believe that the train-boat-train is hard enough for the folks from London and Cambridge. It would be seriously hard work trying to do that from Shrewsbury which is about as far west as you can go in England at that latitude. I'd also forget Hull and Newcastle which are even further away, and going north to go south.

Fly

Uhm, I don't know how much you know about the ferry from Newcastle, but my (very straight laced, and at the time Special Police Constable) sister took it a few years ago and she described it as more or less a 24 hour journey in a combination boat / pub / nightclub...

I'd fly, either from Birmingham or Manchester. It doesn't take long at all, the train from Schipol in to Amersterdam Centraal is very quick and efficient.