Sorry I can't be of any help, but I hope this isn't typical of their behaviour. I have my install this Friday in the 1 - 6PM slot and have also had to take time off of work.
The reason will be because an engineer wasn't assigned to do the job, that is why you didn't recieve a phone call as no one know.
As for you not taking another day off work, you will need a relative there for them to have access to your house to setup the Master socket, Modem, HomeHub and one connection to a PC/Laptop.
Unfortunately, missed appointments are not uncommon these days. Openreach are chronically under-staffed, so if somebody is off sick, or the engineer was given too many jobs to do in one day, then scheduled jobs don't get done.
BT generally have no clue what Openreach are up to, and will keep assuring you that your appointment is still scheduled right up to the point where it's obvious that they aren't going to turn up.
There's not a lot you can do except make another appointment and hope somebody turns up.
With my case... I was booked for phone and infinity on the same day in Nov 2012 as a AM booking. In the afternoon an engineer came and only installed the phone. I only found out that he wan't fitting the bb when he had finished the phone line and said he was leaving. It took over a month for me to get the Infinity installed. It took Many Many calls. A lot of call center staff both here in the UK and abroad told me they would phone back the next day and didn't. When they did, I was told to wait a few more days again and again. No one was bothered. Finally 1 operator said to cancel the order and start again. It worked and I finnally got installed.
Not good as I work at home and had to rely on 3g. I did get some compersation but not enough to cover my costs.
About a month ago my line started to act up. My filter had an issue. BB only worked when I made a call. Had to book an engineer. He came but a few days after he was booked to. He stayed for about 5mins, but couldn't find any line issues. He at least left me a spare filter (which I told him was the likely issue). When the line stopped working again a few days later I changed it and all worked until last night where the same thing started happening again (This is why Im actually online again looking to see if anyone else has had this issue).
But to answer the question. Yes it does look like BT just sends people when they want rather than when it is actually booked. Thats the problem though when its not in-house and rely on external companies.