No road markings on junctions on Manor Gardens

I have often seen traffic split on entering Manor Gardens, then effectively try to pass another vehicle by racing down the other side of side of the central green area. This then creates a very dangerous situation where the 'overtaking' vehicle arrives to merge back in at high speed. Visibility is not very good because of fairly sharp bends, parked cars and pedestrians crossing. This happens because there are no 'give way' lines at the junctions, so this behaviour is seems to be within the rules of the road but when two vehicles find themselves arriving at the same time from different sides of the green, it is not clear what should happen.

It seems to be more dangerous when going East to West, because the 'overtaker' has to start by turning left sharply, losing speed and having to then drive very fast to pull off the overtake they are trying to do, emerging at the junction with Cardinals Walk which is almost a 4 way junction.