Do cheap last-minute holidays still exist?

Every week a Guardian Money reader submits a question, and it's up to you to help him or her out – a selection of the best answers will appear in next Saturday's paper. This week's question: Years ago I remember my family used to book exciting last-minute holidays using Teletext. Do travel agents still discount crazily the day before you're due to fly, or is booking early the way to go? Anyone still doing this; if so, how? Where are the cheapest holidays? What are your thoughts?