Can you explain a little bit more about your project? What is the required accuracy and resolution (e.g., is seconds enough, or do you need better)? What do you want to measure? Where do start/stop events come from? etc.
There are several option of different accuracy, resolution, and level of difficulty. On the 18X access to the internal timer is a bit complicated (peek and poke commands) but can be done. Picaxe 28X1 or 28X2 is friendlier in this regards. For less accuracy required, often a fast counting loop is sufficient. Or you could use an external real-time clock (just a small chip of same size as the Picaxe 08M).
Wolfgang