barney, this dosen't have to be the end of the world.
1. talk to your union rep( if your not in the union, join!), if you don't have a rep or they/you don't think they can handle it, get in touch with your area rep straight away.
2. explain everything honestly and truthfully to your rep.
3. start to put your case together, i would not advise lying/changing your story.
4. do not go sick with stress( unless genuinely suffering from stress)
5. i was hoping to see that you had a good relationship with your manager, but it seems that it isn't great, use this to your advantage. Managers that are over keen to sack an individual often make mistakes in the agreed procedures.Make sure your rep is fully aware of your history of grievance with this manager.(if this gets mentioned a lot during the case the manager dealing with it will get twitchy)
6.So back to the actual event itself, make a big play on the fact that you drove the vehicle back to the office for the good of the company, you believed that get the van back to the office would make it easier to be repaired and that you didn't want to fail the dispatch.( a puncture that didn't look too bad, but got worse on your short journey back maybe a good angle.)
Explain that you feel very silly now and acknowledge that it was a mistake.
make sure you actually apologise for the mistake during early investigation.
7. What did you think you should have done when you noticed the puncture?
have you ever been told what you should do?
is there evidence of the company telling you what to do? ( ie training record, signed by youself)
Hope some of this helps mate, good luck!