Seats in Great Britain can only be booked via a GB booking system because some years ago the RDG (the co-operating operators in GB) decided they didn't need to be connected anymore to any other reservation system. This also means Eurail can't book any seats in GB.

It would have been helpful to mention the exact train you wanted to take (departure time & date) but I suppose it's the direct Avanti West Coast train Holyhead - London. If not, please specify.

The RDG are sending incorrect data about reservations to the European Timetable Centre (where everybody else get their data) and reservation is in fact not mandatory on Avanti West Coast trains. 

Seat reservations in GB are free of charge and can be made at a ticket office in GB, by contacting Avanti West Coast. They can also be made via the GWR website:

Go to www.gwr.com and register for an account (or go directly here; it weirdly doesn't accept spaces in the surname.). 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.

(@Nanja, is there any way you could convince the RDG to send correct data? These questions will come up time and again because of their incorrect data.)

@SarahJaneZ, rvdborgt is right. Reservations aren't mandatory. They are having issues with getting the right data into merits. Our reservation specialist is looking into it with them to look into possible solution that we can help with. I will keep you posted. 

Update: we have reevaluated it and the conclusion is that we can only make changes from our side if they are using train numbers. Unfortunately, they are not so we informed them that the only ways to display the correct information is for them to correct attributes in merits or start with using train numbers. RDG is now looking into the option to update the train numbers.