Call the police, report it as an incident and get an incident number, they might need a brief statement of events but i did this all over the phone, tell them the time and location of the crash, the highways agency website has a list of all work and contractors name and numbers.
Contact the company directly and inform them that their sign blew into road and caused some damage...
I did this when i lost a wing mirror and the door was stratched by a blow over sign on the M1 (one other guy the copper mentioned wrote his car off)
It took about 3 months of pestering (mainly cos they were in the middle of a relocation) but they paid for a main dealer bodyshop to repair the work, was about £800
They are FULLY responsible for maintaining their equipment and ensuring public safety, so they have public liability insurance for cases like this.
Dont let them get away with it .... i didnt and got money
Good luck
J