You will be all right.

With the odd exception of the overnight trains and a very few others, ALL trains in GB are without mandatory REServation-and on the main Intercity lines, like this one, there will be a train at least ev hour. You will see that once IN the train above or at the back of all seats are tiny screens that will show between which stops that seat is taken-or empty if not. It is NOT like an airplane-like so many non-EUR tourists think. It works like that in many, many countries. And the shorter, slower, all-stops regional trains do not even have that-just like the underground metro. The PASS you hold on your fone is the ticket-and that is what will be checked during ride-or in GB often when entering station.

You can also go many more times from LON to Beatles-city by using other trains going north from same station Euston and changing somewhere-like Crewe. Planes over the Ocean often arrive quite late, the britsh entry by their borderpolice may sometime also eat long time, and assuming its LHR you fly into-there are direct trains to Paddington station-then make own way-very expensive metro-ride to Euston (use bankcard to pay) to Euston station for these IC-trains. From LGW its a little bit easier.

Reservations in Great Britain are optional, except for night trains and Eurostar. The app sometimes says there are mandatory reservations for other trains but that is because of errors in the British data.

For domestic trains, you can make a reservation for free at a ticket window in GB or via myaccount.gwr.com. You first have to create an account. (It weirdly doesn't accept spaces in the surname.). Then sign in, and click Bookings at the top. Then look for the “Make a seat/bike reservation“ box. It will look as if you need to select a fare, select any, it doesn't matter (do check 1st or standard=2nd class), continue and make the reservation. It says you won't be charged, and indeed you get the free stand-alone seat reservation without needing to enter any payment details. Even though it's GWR, this works for any route where seat reservations are available.

Thank you so much for ansewers. You helped me a lot!!!!