Thank you for all the responses. I think some of the responders may be missing my point, and have been making several assumptions. (Including one about my gender!)
Firstly, I do not ride that erratically, and I am probably riding (on the level) at between 10 and 12 mph (according to my new computer!).
Secondly, the Durham Railway Paths are used my many people not just cyclists. There are people with dogs, people of all ages, from young children in pushchairs, older people in power chairs, people on horses, and people just out for a walk and/or a chat. The paths are not dedicated to cyclists, and cyclists need to behave accordingly.
Thirdly, humans as a result of our evolution, react quickly to something in our peripheral vision. Something suddenly appearing in the 'corner of our eye' is likely to startle us and stimulate immediate involuntary reaction.
Common courtesy is therefore very important. The County Council Rules are that cyclists should give way to pedestrians and horses, but it is common sense to give warning of where you are. (I am always very careful around horses!) I always greet people anyway. Courtesy costs nothing.
Yes, I may have to get a mirror, but quite frankly having to 'check my six' constantly makes me nervous and distracted, and I do not see why this should need to be.
Anyway, in my 16 miles yesterday, everybody I met was polite and cheerful. As it happens nobody overtook me, but all the cyclists I spoke to were of the opinion that the 'unwarned overtaking' problem has been getting much worse recently.