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The Law
An organiser is entitled to specify or restrict the sale of any goods, but these conditions must be unambiguously defined, and  if there is likely to be any confusion should be given in writing to each trader. No alterations to the contract should ever be made without informing the traders well in advance, and giving the opportunity to withdraw together with the return of the stall fee and possibly offering compensation.

However, the law also states specifically that care should be taken to ensure that a trader is not given cause to complain that he has been treated unfairly or in an arbitrary manner
(P & C 5th edt. page 113)
In practice the rest of the legal requirements are mainly to do with the obvious factors of health and safety and trading standards, but there are also some minor but important points regarding right of access to stalls.
Technically most events are Fairs, as the definition of a market is that it is for the sole purpose of selling goods. Fairs also offer entertainment, contests etc.  Fortunately, the distinction is academic, as exactly the same laws and regulations apply to both markets and fairs.
The usual procedure is that once traders know that an event is to take place then, if they want to take part they will apply for a pitch. The organiser then invites those traders that seem to be the most appropriate for the event.
When traders come to a site in order to sell goods this constitutes a Temporary Market and becomes subject to the Laws of Markets and Fairs. Commonly known as Pease and Chitties.
However, as this initial agreement is in practice a legal contract, it is ESSENTIAL that at this stage each party should be fully informed as to the type of event, the likely appearance of the stall and the class of goods to be sold.