Travelling from London to Edinburgh/Edinburgh to Amsterdam

By day it's a bit over 4 hrs. By night it's the Caledonian sleeper. Refer to http://www.seat61.com. Cheapest tix are those booked as far in advance as possible; tix go on sale about 12 weeks before travel, so keep checking.

As for getting to Amsterdam, you'll probably find the cheapest and quickest option are the same; flying. Refer to http://www.easyjet.com. Again, book as far ahead in advance as poss for cheapest tix, only diff is 12 week rule doesn't apply, tix are already available for August for flying, prices start from £40.99 one way per person and include all fees apart from baggage, booking and credit card fees (which are made extremely obvious at point of paying anyway).

Ferry journey (overnight) looks good value, but for August (high season) you should book soon. Ferry actually departs from North Shields, just east of Newcastle city centre, but near Meadowell and Percy Main Metro stations.

Will need to book train tickets soon as well for good price- end of UK summer holidays in late august (actually, think scotland might've gone back already, but will still be packed). I've done the ferry before and liked it, but won't save you any money over booking cheap flights ahead though. But is an experience, free night's accomodation each way. (Having said that, it does have half of Newcastle drinking crazy amounts on there- the bar is a sight to behold at 3am...)

You can catch a ferry from Edinburgh (Rosyth) to Zeebrugge and then a train from there to Amsterdam.

Also, the place where the ferry goes from in Newcastle is a hole. Got the taxi out there and driver reckoned taking the metro there (with a 30min walk) was a pretty quick way to get mugged

The Rosyth to Zeebrugge ferry is now freight only.
Going by train betwen London and Edinburgh is not much slower city centre to city centre taking into consideration travel to and from airports, and check in times etc.
If you haven't booked accommodation in Edinburgh do it now.

Flying will most likely be cheaper. There are plenty of cheap flights from London to Edinburgh both on BA and the various discount/regional airlines. If I remember correctly it was about 4.5-5 hours by train from Edinburgh to London Kings Cross, back when I took the train quite often. But these days if you book your flight ticket in advance it's often cheaper, even when factoring in the cost of the local transit to the airport.

If you're doing a London - Edinburgh - Amsterdam - London trip, flying will most certainly be the most efficient and probably most cost effective solution. Book separate tickets on Easyjet from London to Edinburgh, and from Edinburght to Amsterdam, and from Amsterdam to London.

Train to Edinburgh makes a nice daytime journey if you're starting from central London and you get to see a good bit of the countryside.

Not much point in flying unless you were out at the airport anyway.

By the time you get to Luton airport (for example) you're about 1/4 of the way to Edinburgh in time terms, then there's check-in time and baggage collection at the other end etc. Not to mention the cost of travel to/from airports.

Then get easyjet from Edinburgh to Amsterdam.

We took the Rosyth ferry to Zeebrugge last year and really enjoyed it but now that it's discontinued, it's not worth trekking back down to Tyneside to take it. It takes about 18 hours all in and isn't cheap.