I used to ride just about anywhere .... London, Birmingham, Bristol, through French and Belgian towns, in the Alps etc without ever worrying about traffic, but as I'm getting older and slower and my wife's health issues require me to remain healthy and uninjured, my attitudes are changing. Large parts of England seem to be becoming built over with dual carriageways, large roundabouts and fast slip roads that put me off even thinking of riding my bike there.
I find myself being a lot more selective in where I ride these days. I mostly ride the quiet country lanes of Severnside, avoiding the school run and other busy times, and I have stopped doing some of my other local rides altogether due to the traffic. I'm lucky enough to have a car .... allowing me to head slightly further afield for my rides and I am able to afford regular mini breaks in different parts of the UK, so I know I am fortunate in that respect.
For anyone on this forum who is able to travel around the country (or abroad) and take their bike with them, I can highly recommend some places with great cycling to be had and very little traffic. Some that spring to mind are, (in no particular order), The Llyn Peninsular in N.Wales, Moray in the North of Scotland, The Rhins of Galloway, The Isle of Wight, The Yorkshire Dales (out of the holiday season), and some lovely rural traffic-free trails such as the Mawddach Trail and The Tarka Trail. I am about to try out some of the trails in the Peak District this week as I've heard good things about them.
In the past I have always found the roads of rural France to be extremely quiet, and the local drivers very courteous to cyclists. The RAVel network of cycle trails in Eastern Belgium is absolutely magnificent, allowing you to pootle safely from town to town away from the traffic, but with every facility you could want all close at hand. I appreciate that not everyone has the option to try it out though.