The business needs to be registered with the Environmental Health department of the local district council where you intend to trade (or unitary/metropolitan council, as appropriate), not with your county council.
All staff must have obtained Food Hygiene Certificates, at Level 1 or higher.
Those are the easier hurdles to overcome. The trickier one is that anyone selling while on a public highway (which includes associated verges and footpaths), or selling to people who are on such a public highway, needs a street trading licence. Unlike the matters to referred to above, that's discretionary and not all councils issue them easily.
If you plan to trade by the roadside you need to note additionally that the police often object to vans trading in laybys, particularly when doing so increases movements in and out of a layby on a busy road (thus adding to traffic hazards along that road).
Some mobile catering vans, however, are located on private property (where their customers are also on private property and not on the highway). You don't need a street trading permit under such circumstances but planning permission, for a change of use, may then well be needed. (Again, that's dealt with by district councils, who can advise you). You of course need the consent of the land owner.
If you plan on serving hot food or drink between 11pm and 5am you also require a Premises Licence.
Chris