Just to note, though, that you can book tickets with Trainline, which you can't with traintimes.org.uk, it does have limits :) However, Trainline charge a booking fee – https://ehelp.thetrainline.com/app/answers/popup_detail/a_id... – and so I would suggest using any train operating company site (they all sell nearly all tickets), whichever one you find most agreeable.
By contrast traintimes.org.uk is simple, highly usable, small, accessible, respectful of privacy and works as plain html.
For me it's an easy choice but your mileage may vary!