My parents are due to fly over to me around that time
Travel Advice : 9th - 12th June : Download Music Festival
For customers travelling to or from the Airport between Friday 9th June and Monday 12th June, please be aware that you may experience heavy traffic or some delays around Nottingham East Midlands Airport and Donington Park. This is due to the Download Music Festival taking place during that time.
Anyone travelling to the Airport is urged to allow plenty of extra time for possible delays. All passengers are advised to check-in at least two hours prior to departure. Traffic management systems and temporary traffic lights will be in operation around the Airport, the A453 approach and near to Donington Park. Please drive with caution, follow any diversion signs and take note of any traffic management signs which may indicate a change in traffic management plans.
I went to Download a few years ago and I do believe they were directing the festival traffic off the M1 the junction before East Mids Airport which didn't cause too many problems to the airport traffic. Wouldnt worry about it too much!!