LONDON—More than 20 shellfish trucks parked on roads near the British parliament and Prime Minister Boris Johnson’s Downing Street residence on Monday to protest against post-Brexit bureaucracy that has throttled exports to the European Union. Many fishermen have been unable to export to the EU since catch certificates, health checks, and customs declarations were introduced at the start of this year, delaying their deliveries and prompting European buyers to reject them. Trucks with slogans such as “Brexit carnage” and “incompetent government destroying shellfish industry” parked metres from Johnson’s 10 Downing Street office in central London. “We strongly feel the system could potentially collapse,” said Gary Hodgson, a director of Venture Seafoods, which exports live and processed crabs and lobsters to the EU and had trucks parked near Downing Street. “Prime Minister Boris Johnson needs to be honest with us, with himself, and with the British public about the problems for …