I have the same pet carrier as Fluffagrams
And have also used it for train travel - it's a much better option than a cage as your hamster will be more secure (plus it's easier to carry and have on your knee). As Fluffagrams says it's a good size to fit a little house in. I half fill it with substrate, hide various treats and bits of food among the substrate, and put some torn up strips of plain white toilet paper in - our hamsters have usually built a little nest while in there. And some sort of small house so your hamsters can feel safe and hide away. I used to have one of the little plastic pod houses from the hamster heaven in mine - it's a bit small but open underneath so they can burrow down. Have also had one of the Rosewood cardboard hay houses in there (just fits with a bit of space) - but a cardboard box - eg tissue box cut to size - is fine too.
Also put a piece of cucumber in so your hammy can keep hydrated during the journey.
I have done that journey many times as my family live on the south coast and I live in the North East. It means changing in London which is the hassly bit. After that the train from London north is fast and no more than 2 to 2 and a half hours depending how far north you're coming!
I would recommend paying an extra £15 to £20 to get a taxi from either Charing Cross or London Bridge - wherever you get off - to Kings Cross. You get there quicker and less noise and less chance of dropping things or being knocked. It makes the journey a whole lot easier and I've often found I've picked up an earlier connection doing it that way. Although that wouldn't work if you've booked a specific train. I tend to pay the full price for an open ticket so I'm not dependant on getting a particular train as it helps to shorten the journey if you can get an earlier connection. If you have a railcard it helps reduce the price of that quite a bit and you don't risk being stuck on a platform for ages if the train you've booked is cancelled or has broken down or something.
There are also limits when you can travel in and out of Kings Cross so best to do the journey in the morning (I think the limits are 2pm to 7pm). That would also be better for your hammy too. As they sleep through the day normally then setting off early and arriving mid afternoon would be a better journey for a hamster - and you can then settle them in a cage before night time at the other end.
Ours have always just slept in the carrier the whole time
Although the longest train journey I've done has been 2 to 3 hours but it was fine. I always take a small fleece blanket and have the pet carrier on my knee with the blanket over it so it's dark inside and less disturbance. Although keep an eye on that as our current hamster Newt once chewed a hole in the blanket through the holes in the pet carrier!
The biggest thing to watch out for is interested people wanting to know what's in there and wanting a peek - and that can be stressful for the hamster so best to politely say - sorry he's asleep best not to disturb.
I would definitely recommend getting that Ferplast Aladino in the Guinea pig size. There are similar sized pet carriers but that one has a wider base at the bottom so it's more like a mini cage. It's also quite secure.