The biggest climbs are probably only 3-4% average overall, but some do have short ramps in them that will get near 8-9% in parts. Those parts are less than 50 metres long though and few and far between. I think the problem is that RWGPS does tend to average out the gradients on short climbs so you don't see them reflected accurately.
EDIT - found some segments on Strava that are a little more representative of what you can expect:
Bullock Road @ 4.5 miles in -
https://www.strava.com/segments/4927498
Caldecote @ 9 miles in -
https://www.strava.com/segments/15151768
Salome Wood @ 20 miles in -
https://www.strava.com/segments/1065396
Vinegar Hill (Alconbury) @ 31.5 miles in -
https://www.strava.com/segments/1007971
Parallel to A1(M) @ 38 miles in -
https://www.strava.com/segments/8208905
Haddon Hill @ 94.5 miles / 5.5 miles to go -
https://www.strava.com/segments/1005438
I think that's all the major ones - as you can see, there's really not much to fear there, even on a singlespeed.