Most of the local babies are under the care of the health visitor clinic at the Marylebone Health Centre on Marylebone Road. The clinic s held once a week on Tuesdays from 2-4pm. A similar clinic runs at Micky Star in Paddington, though I am not sure what the current times are.
The main surgeries in the area are the Marylebone Health Centre, the Crawford St surgery and the Cavendish Health Centre. You can find your local GP on the NHS we site here . Connaught Square Practice is also nearby on Connaught Square, W2 - they run a weekend walk-in service (see below).
Of course there are plenty of private GPs in the area along Harley St and the surrounding streets as well as the Portland Hospital.
Connnaught Square Practice runs a walk-in GP and nurse service on weekends from 10am to 6pm. You do not have to be registered at the practice.
St Mary's Paddington has a separate (NHS) A&E for children which means you do not have to wait in the main A&E. You have to check in at the main A&E section but will then be directed to a separate area. More information here.
The Portland Hospital has 24 hour care available for children privately. More information here.
They also provide antenatal classes run by Lullaby which are very comprehensive. http://www.marylebonemums.com/blog/lulubaby-antenatal-classes-at-portland-hospital
St John and St Elizabeth in St Johns Wood also has a 24 hour GP service for private care. More information here and also on Casualty First from the age of 1 here.
Osteopathy The College of Osteopaths is conveniently located just next to Marylebone station, at 8-10 Boston Place, London NW1 6QH. They have a Training Clinic on site which provides osteopathic treatment at reduced rates. The treatment is carried out by senior students supervised by registered osteopaths for a much reduced price (currently £25/appt as of writing). You can find out more information at www.collegeofosteopaths.ac.uk, or call 020 7723 6478. The clinic is open on Tuesdays and Thursdays.