Within the UK driving is the cheapest but train is the next best if you're not driving.
For example I just stuck in Lincoln > London on trainline.com for 2 weeks time and a return ticket for 2 adults is £92.80. But you can shop around or get a railcard to get the price down.
In terms of European cities, you can actually get the train from London to Paris or Amsterdam on the Eurostar, worth looking into that. Other than that yeah you can get flights to anywhere so you could train ticket to London > Flight to Europe if you don't mind splashing a bit of cash. There are other airports not in London but an Airport like Heathrow would give you main options, but again just need to shop around a bit to see what's best for you.