Switching broadband, engineer misses appointment and claims could not get access to property

Kavajo

I am in process of moving from Virgin (no complaints re service but too expensive after intro contract ended) to Vodafone. An engineer was booked to come between 1 and 6pm I took a day off to stay at home. I was in my front room from 1pm onwards with a good view of the road outside. I kept myself busy by cleaning the windows at the front. It got to 5 and there was no sign of the engineer. No phonecalls or anyone coming to the door. I got on the Vodafone chat to see what was happening, but it was a complete waste of time, cutting me off several times and forcing me to restart with security verification again. I gave up after 90 minutes of frustration. 
Today, Monday, I called and spent a long time on hold before speaking to a real person. The agent looked at my notes and told me the engineer called me several times and was not able to access the property. Incredible. I explained that this was not correct as I waited very deliberately with my phone and ready for the visit. 
Has anyone else had this happen? It seems to me the only reasonable explanation is that the engineer has lied. There were no calls and no visit. Perhaps when there is too much work scheduled, this is how they skip an appointment. 
I'm being offered automatic compensation under some scheme - £26.24. But when I looked at the mail from Vodafone they say they charge customers £110 for a missed engineer appointment. Surely that is an unfair contract? Anyone had a similar issue?