I lived in Coventry for 20 years but I didn't hear of the Lickey Hills until about 20 years after I left. (I didn't used to look at OS maps back then. These days, I am forever studying different parts of the country and planning future rides.) I have still never been to them, and may never get round to it now since visits back to the Midlands with a bike are becoming increasingly rare.
I get that a lot on my singlespeed bike, which gives me no assistance at all over TDC, unlike the chain on fixed. I have modified my pedal stroke by dropping my heels before TDC to allow me to push the crank more from the back rather than the top. That helps but only up to a point. I can manage short stretches of 10% but not much steeper than that, and only for a couple of hundred metres.
That's why I put a triple chainset and biggish cassette on my best bike - I can get up about 99% of UK climbs in a 28/30 bottom gear.