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The game at Wembley is likely to finish at around 1700 BST - or longer if extra time and penalties are required - which is unlikely to allow enough time for the estimated 200 coaches and thousands of cars to have passed through.
Detours will be in place advising light vehicles to use the B4042 and A429 via Malmesbury, and heavy vehicles to use the A3102, A4 and A350 via Calne and Chippenham.
Supporters club guru Vince Alm said: "They [the Highways Agency] obviously didn't know we were going to be in the play-off final that weekend.
"When they apply for a motorway closure it takes a couple of weeks to plan. It's just unfortunate.
"We will assess it in the next day or two and we may not choose to come back that route. We may choose to use the M40."
A Highways Agency spokesperson said: "The closure of the M4 to install a new overbridge at Summerlands near Chippenham has been planned for for some time.
"Before closing the motorway on Saturday evening our contractors will assess the traffic flow levels to determine when to implement the closure.
"We ask that drivers take extra care when travelling along the clearly signed diversion routes."