Deutsche Bahn has been given the okay to run trains through the Eurotunnel to London. It will start in 2016. The big question is: will the train from London to Frankfurt be faster than a plane when considering city center to city center? http://www.businesstravelnews.com/Business-Travel/Deutsche-Bahn-received-operating-certificate-to-run-passenger-services-from-London-through-the-Channel-Tunnel/?ib=Rail&a=trans
You can currently travel from Frankfurt to London with a change of trains (to the EuroStar) in Brussels. What this means is that, in 2016, you will be able to travel direct (no change) to London on an ICE. There will probably also be an advance purchase, Europa-Spezial fare available for that route.
The estimated travel time is 5 hours. DB also intend to run direct services to Amsterdam (4h). This is without consideration of the possibility that passengers would have to get off to go through immigration at Lille.
This is without consideration of the possibility that passengers would have to get off to go through immigration at Lille From what I understand the Chunnel trains going to Amsterdam would terminate at Amsterdam Zuid station instead of Centraal where there is room to build an immigration hall. If it's not built in time immigration agents would board the train en-route and do checks while the train is moving. http://www.connexionfrance.com/Channel-Tunnel-Chunnel-Deutsche-Bahn-Eurotunnel-14794-view-article.html