I know the area well but it has changed alot since 1961 that's for sure. Not that I was around in 1961 but I grew up not far from Paddington and know alot of people who were originally from that area. Also, it was the hospital where most mothers gave birth to their children whilst I was living in nearby in North West London. I was born in Ireland but one of my brothers was actually born in St. Mary's Hospital.
If your mother was born in 1961 I'm almost certain
St. Mary's in Paddington is where she would have been born.
Home - Imperial College Healthcare NHS Trust Internet
I think there was another hospital in Paddington but this may have been a temporary replacement whilst St. mary's was being renovated. And the renovations took place in the mid-70's from what I remember. I know this because I remember seeing a friend's birth certificate and asking him why his wasn't St. Mary's like most of the children round our way. The reason it simply stated 'Paddington' was most likely the temporary replacement though I will try to find out more information if I can. By the way, just because your mother was born in Paddington doesn't mean she necessarily resided in Paddington. It was a frontline maternity ward that serviced a large section of the Edgware Road and West-North-West London. Anywhere from Edgware Road, Paddington-Maida Vale and Cricklewood. Don't take these boundaries as fact, but I'm sure the maternity ward there covered a large region, including the area I grew up in.
I know people who've known that area alot longer than me and my recollections are a bit hazy. I'm not even sure Paddington St. Mary's even has a maternity ward anymore but I hope that the hospital will be able to give you some information. I will be back to add some more information if I can get some more substantial historical facts. Good luck.