I think each council has there own slightly different policies. Most require you to have a srett traders license and planning permission for to use the actual site, plus anyone working in the van has to have a street traders employee license. Also require a enviromental health certificate and a gas safety certificate. Plus public liability insurance
But where I am nort sure is if you are set up on private land with landowners permission, you might not need the traders lisence but probably still the planning permission, (so all the local cafes can object).
I will be mainly at events on private land where the planning and buildings permission should cover catering units.
One good way if you are new to it all is to buy an existing business not just the van, ie you take over their plot. This can be more expensive so make sure the plot is good for making money, they might be selling up due to bad turnover.
Try your local council site again for info, under permits or planning perhaps. Try searching neighbouring councils site they might have more info and should be fairly similar, I found the environmental health dep were very chatty and helpful and should be happy to go through the basics to look for in a van, might even have a specific leaflet.