New 20 MPH speed limit to also apply to bikes in Southwark

How can you find out which roads are controlled by council and which are TfL.

Where I live in Peckham people drive like absolute belms around quiet back, residential streets and I can't wait to see a 20mph speed limit introduced.
If you think of it like a body, the Council manages all the capillaries and veins (often roads with yellow lines), while TfL controls the main arteries (Red Routes).

These are the Red Routes in Southwark (you can see how debates arise between TfL and Council over who designs/improves the dangerous junctions):

Borough High Street, part
Old Kent Road
New Kent Road
Tower Bridge Road
Southwark Street
Blackfriars Road
Tooley Street
St George's Road
Druid Street, part
London Road
St. Thomas' Street
Great Dover Street
Jamaica Road

More here if you're unsure: https://www.tfl.gov.uk/modes/driving/red-routes/rules-of-red-routes

I agree with you. McNeill is really bad, for one example.