This is the official Jubilee Greenway cycle route from Tate Modern to Westminster Bridge (note it includes the Blackfriars Bridge approach which TfL want to make 30mph):
Just after the Tate Modern cyclists follow a different route to the end of this section as the path alongside the river is closed to cyclists. Turn left onto Hopton Street after the Tate Modern and then right onto Southwark Street. Turn right onto Blackfriars Road , heading North towards Blackfriars Bridge, but turn left into Upper Ground just before you cross the bridge.
Pass the National Theatre on the right and head under Waterloo Bridge continuing along Belvedere Road. With the London Eye directly to the right, turn left onto Chicheley Street. At the end, turn right onto York Road. To reach the official end point of this section, follow the road around and turn right towards Westminster Bridge where this section ends. Alternatively, to continue onto section 9, continue ahead onto Lambeth Palace Road towards Lambeth Bridge.
Pass the National Theatre on the right and head under Waterloo Bridge continuing along Belvedere Road. With the London Eye directly to the right, turn left onto Chicheley Street. At the end, turn right onto York Road. To reach the official end point of this section, follow the road around and turn right towards Westminster Bridge where this section ends. Alternatively, to continue onto section 9, continue ahead onto Lambeth Palace Road towards Lambeth Bridge.
This is my photo of the York Road part today. What a delightful Greenway.
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