I can remember there being an early morning train on Monday - Friday that ran Birmingham New Street to Euston, with a northbound return in the early evening.
This train was named "The Birmingham Pullman" with the only intermediate call between New Street and Euston being Birmingham International, meaning that this was the only InterCity West Coast train that did not call at Coventry.
The standard pattern was Wolverhampton, Sandwell & Dudley, New Street, International, Coventry, Watford Junction, Euston every 60 minutes, and New Street, International, Coventry, Milton Keynes Central, Euston every 60 minutes. On Sundays, I think there may have been an additional call at Rugby.