Yes that is true, my now deceased uncle’s "war bride" Margaret was from the southeast of Britain, and she mentioned to me that the birds called "robin" in her area were smaller than ours. I looked in Wiki, and they had an article on the "robin" and the name as used in different areas. The European Robin (Erithacus rubecula), most commonly known in Anglophone Europe simply as the Robin, is a small insectivorous passerine bird that was formerly classed as a member of the thrush family (Turdidae), but is now considered to be an Old World flycatcher (Muscicapidae). Around 12.5–14.0 cm (5.0–5.5 in) in length, the male and female are similar in colouration, with an orange breast and face lined with grey, brown upperparts and a whitish belly. It is found across Europe, east to Western Siberia and south to North Africa; it is sedentary in most of its range except the far north. The term Robin is also applied to some unrelated birds with red or orange breasts. These include the American Robin (Turdus migratorius), which is a thrush, and the Australian red robins of the genus Petroica, which are more closely related to crows. See: European Robin - Wikipedia, the free encyclopedia
Yeah, they are smaller and browner without the line above the eyes, other than the red breast they fit nicely into the British LBB (Little Brown Bird) catagory.