Firstly though, why is Brook Drive a rat-run in the West-East direction? Google map directions reveal all. Drivers from Westminster Bridge or Lambeth Bridge to the Walworth Road are directed via Brook Drive and Dante Road rather than the designated A roads.
The immediately neighbouring enclave of back streets, in grey below, around Walcot Square and St Mary's Gardens are very much calmer and quieter. Many years ago the residents persuaded the council to install the gate (marked by the short, thick black line) at the junction of Sullivan Road and Brook Drive to prevent motor-traffic cutting through their streets.
Turning that gate by 90°, to the pink line, would create two cells - part of Brook Drive would become part of the Walcot Square quiet enclave - still able to get to and from their houses while enjoying the benefits that their neighbours have had for years. The other half of Brook Drive would be part of a newly calmed enclave of streets gaining the same or similar benefits.
As well as enabling the residents of Brook Drive and Dante Road to have less noise, danger and air pollution, such a measure would increase the freedom for local children attending the local Charlotte Sharman, Archbishop Sumner and Crampton primary schools to easily walk or cycle to school at minimal risk.
Turning the barrier may not be the ideal, or the whole, way of creating a back street area free of traffic that should be using the main roads. There may be a better location to install the traffic filter on Brook Drive. And there's a likelihood that some rat-running would relocate to use Wincott Street / Renfrew Road (the thin black line) so it makes sense to consider options and implement appropriate measures within the entire cell of back streets bordered by the A roads. I welcome suggested alternative options or additions in the comments section.
This traffic filtering scheme (and similar ones you may think of) would fit well into the current Lambeth consultation for this area - if you like it please include it in your response. I hope that Lambeth will accept responses from residents on the Southwark side of Brook Drive too.