The project was expected to be completed by March 1971 but on 2 June 1970 a 230-foot (70 m) cantilever being used to put one of the 150-tonne sections into position collapsed on the south side of the estuary.

[4] These rules laid the groundwork for a new British Standard covering box girder bridge design.

The ferry service between Hobbs Point and Neyland ceased when the construction of the Cleddau Bridge was completed in 1975.

Toll booths with barriers were introduced in September 2004 to reduce the number of vehicles driving through without paying.

Vehicles taller than 1.9 m (6 ft 3 in), bicycles and motorcycles are usually not permitted to cross the bridge when wind speeds exceed 50 mph (80 km/h).

[13] A memorial plaque to the four men who died in the bridge collapse was unveiled on the 25th anniversary of the disaster in 1995, but was reported stolen in 2017.