My local station is one of those in West Yorkshire which would come under the subsidised "Regional Railways" category. Services are heavily used during the rush hour and fairly well loaded during the day (particularly so throughout Saturday). Sunday we have a 2-hourly service which is usually well used - although less so when compared to the rest of the week which is not surprising considering the inconvenience of trying to work around 2-hour intervals.
I've always thought that an hourly service would attract quite a few more passengers, and this impression was re-enforced recently when I travelled on a re-instated mid-day Sunday service from Wigan to Manchester via Atherton. Even though the hourly Sunday service had only been re-introduced within the past few months after around 40 years with no Sunday trains at all, the train was pretty well loaded with plenty of passengers joining at all the major stops (Atherton, Swinton and Walkden).
I suspect that this is the case in many such areas.