There are also overnight trains between London and Edinburgh and various other places in Scotland - and the kids may really get excited about that option - you could book a 4-person private compartment or two 2-person private compartments adjoining each other - with i think but not sure a door in between them.

These are called the Caledonia Sleepers - running every night except Saturday - i have taken them several times and found them very very comfy. A railpass would work on them as well but you'd have to pay extra for the sleeping accommodation of your choice (several types to chose from)

Caledonian Sleeper trains | ScotRail
Buy train travel tickets for the ScotRail Caledonian Sleeper Trains, overnight train services operating between London Euston and Scotland.

Book online - Bargain Berths - Timetables - About the sleeper
www.scotrail.co.uk/caledoniansleeper/index.html

Caledonian Sleeper Train | About the sleeper | ScotRail
Caledonian sleeper facilities include single and twin berth cabins with comfortable beds, blankets and fresh cotton sheets as well as air-conditioning and ...
http://www.scotrail.co.uk/caledonian...e-sleeper.html - Cached - Similar
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It's a tough choice, we are leaning toward a week London, a week in Bruges/Burgundy if that is possible and a week in Paris.>

I think that is a great itinerary - Take the Eurostar train from London to Brussels and with the ABS or All-Belgian-Stations aspect of the Eurostar ticket you can go on free to any Belgian station - ending up in Bruges at no extra cost.

Bruges to Burgundy means probably going back thru Paris - take a local train from Bruges to Lille-Flandres station - then a TGV train to Paris-Nord - transfer to Paris Gare de Lyon and be in Beaune in about 2.5 hours (from Paris) - there could be a routing via Brussels not going thru Paris but that could take much longer.