Copyright isn't relevant here.
There is nothing to stop filming in a public place, and a person entered in an event has no expectation of privacy.
Broadcasting said film changes that.
However if a person can be identified from the footage and they are the main subject (not incidental and in the background etc) it is personal data(the test is usually two identifiers e.g in this case the image and a number board) then Data Protection applies, and you have to have the relevant consent to use that image.
So if you have the appropriate permission from the organiser, who has informed the entrants that they will be filmed and to what purpose the images will be put and they have agreed, then you are golden.
You might want to have a look at Ofcomm guidelines, the ICO website and Outlaw.com as mentioned above is a good source.