Safe cycling routes

I have just discovered this site whilst looking for a safer route than the one I have been using for one of my regular rides, after suffering multiple injuries in a road collision on a Roundabout.   I should say I have used my existing route for many years without previous incident. 

The recommended route covered areas I know well.   Much of the route is not passable.  The initial recommendation, from my home, ignored a safe park road and quiet residential road in favour of a route requiring two right turns onto and off a busy single carriageway road with heavy commercial traffic.  Whilst recommending the use of a non-existent cycleway. 

I'm not sure how safe that route would actually be.