Before Eurostar moved to St Pancras, I travelled between Liverpool Street and Waterloo by taxi on several occasions. It usually took around 12 to 15 minutes. (The times stick in my head because the fare was usually between �12 and �15. i.e. equivalent to �1 per minute). However, I was always travelling either very early in the morning or very late at night.
During the rush hour, you'd probably need to allow at least 20 minutes (and expect a proportionately higher fare - the meters in London cabs click over at an alarming rate when the cab is stuck in traffic).
The only reason I took a taxi early in the morning or late at night was because the Waterloo & City Line isn't open at these times. During the rush hour, the total journey time (via Bank) is 13 minutes, with trains running every 3 minutes, so its quicker than taking a cab. If you've got a rail ticket with the � (or +) sign printed on it, it's valid for cross-London travel on the Underground, so it won't cost you anything extra. Otherwise a single journey is �4.
Chris