An update: I did some research today. I got my Cycle Analyst working again and I went out and tested myself and the machine against some hills.
To make it worthwhile though, I needed to measure the hills. I had the offer of a very serious digital angle measurer, as used to align the wings on aircraft, but I thought I would start with something simpler, even if it is only accurate to a degree or two.
At this stage, this is still with the standard gearing. Most of the hills I have been going up turn out to be 4 to 6 degrees. Six degrees doesn't sound much but looks alarmingly steep when you are there - I suspect it is the maximum that street planners will generally allow.
I did find some 8 to 9 degree hills out in the countryside and I can cope with those. In bottom gear and with a half used battery I can maintain 11 to 12 mph. I'm not sure for how long, though.
Then I finally found a good one. It measured as 11 degrees one way and 9 the other, so let's take it as 10. I can just do this at 9 mph. But I really would not want to do a long one of this slope.
What this does mean though, is that when the gearing is changed, I stand a pretty good chance of doing the magic 11.3 degrees while keeping the speed up. 11.3 degrees is a slope of 1 in 5, which is going to be encountered in the TofB.
Also, I found that on a gentle slop, with my top cadence in bottom gear, I can get to 16 mph. That gives me the info I need to calculate a new front chainring size for hill climbing.
Nick
Edited to add: I had a PM asking for details of the inclinometer. These types are used in building work; do a search for "angle finder" or "angle setter" and you will find a range of them. The one I have is a bottom of the range one made by C&K; it costs about £7 from various suppliers. Its a bit crude but it did the job. I drilled the two holes for the cable ties.