Yes, you can just about do London to Copenhagen in one (long) day. Do you have any particular route in mind?
Eurostar to Rotterdam (reservation required)
Several IC and ICE to reach Hamburg
IC to Copenhagen (reservation required in Summer months)
Yes you can do that but it’s a long journey. I’d recommend spending a night in Hamburg or on the Hamburg - Copenhagen night train. It arrives quite early in the morning though (only one pass day used as the departure day counts).
On a pass day you can take as many trains as you want. On 2 of those pass days you can travel in your own country.
Remember that the Eurostar requires a mandatory reservation : 30€ to Paris, Lille, Brussels and 35€ to Rotterdam, Amsterdam. It’s a popular route and there’s a passholder quota so book well in advance. What would be your travel date ? Check availability here : https://www.b-europe.com/EN/Booking/Pass#TravelWish
As a good alternative there’s the daytime or overnight Harwich - Hoek van Holland (Rotterdam) ferry : 30% discount with Interrail.
The vast majority of trains can be booked online. Exception : some Spanish regional trains and trains in Romania, Bulgaria, Turkey.
Questions welcome. :)