I'd say it is a de Dion Bouton, probably 6 h.p. single cylinder and brand new! BY is a Croydon registration code and this one is no longer in use but the Veteran Car Club Dated the car registered BY 509 as a 1904 6 h.p. de Dion Bouton.
The car has what we call a tonneau body with seats behind the driver and front passenger. There were two types of tonneau, depending on the access to those seats. The "rear entrance tonneau" had a door between the back seats and the "swing seat tonneau" had a front passenger seat that could be swung aside to leave a passage to the rear. I can't see which this is.
Interestingly the owner has spent a lot of money on lamps, which were accessories in those days, but has not added a windscreen - the absence of which makes motoring beastly even in good weather.