In general with rail tickets in the UK it is not so much about where you buy them as when you buy them and what restrictions you are prepared to have.

"advance" tickets can be significantly cheaper than "off peak" or "anytime" tickets but they must be bought in advance and they lock you into a specific train. They are also not available on all routes (I don't know specifically about the route in the question) and are limited in number.

"off peak" or "anytime" tickets will be the same price whenever you buy them and they aren't limited in number.

If you look carefully on the websites they will usually tell you what exactly they are selling but they don't like to make it too obvious.

It is difficult to predict whether your plane will be on time or how long it will take to get through immigration and customs. So if you buy an advance ticket you will need to have substantial padding in your schedule. Personally I rarely buy advance tickets because I do not consider the cost saving to be worth the inflexibility and the extra waiting around.

Be careful when buying online, some sites (notably the trainline) will charge extra for "booking fees" or "delivery". These charges will be on top of the price for the ticket itself.