Anyone else had a similar experience with a taxi firm?

I phone for a taxi, asking it to arrive at [time] (later the same day). Give details, name address, destination etc.

At [time-5mins] I go out into the street to wait for the taxi. And wait. And wait. And wait.

At [time+25 mins] I go back inside and phone the taxi company to ask what happened. They tell me they didn't send the taxi because 'I didn't answer my phone at [time].'

As a result of this I missed my train and was late for a gig I was going to...