Plans have been submitted to demolish Laycock House and the adjacent former Children's Services property between Albert Road, South King Street and Charnley Road.
Planning permission is being sought to use the site as a car park with a total of 105 spaces once the buildings have been bulldozed, for a period of up to three years.
The register office was the site of many weddings over the years but ceremonies have been held at the Wedding Chapel on Central Promenade since it opened in 2012.
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Kelly Goudie and Simon Garrick exchanged vows on January 12 2012, and since then around 5,000 weddings have taken place in the chapel – with another 350 booked in for 2022.
The wedding chapel is part of the same building which houses the tourist information centre.
Prince Edward officially opened the whole complex when he visited Blackpool in February 2012 as part of the Queen’s Diamond Jubilee celebrations.
Staff from Children's Services who occupied the offices on Albert Road have also been relocated, leaving that property empty.
Demolition of both the offices and the former register office will enable 51 additional spaces to be added to the existing car park, bringing the total up to 105.
Both buildings date back to the early 1980s when they were commissioned by Lancashire County Council, which ran services in the town at that time.
If planning permission is granted, the project will become the latest in a series of demolitions to create town centre car parks.
In 2015 the former Syndicate nightclub, which the council had bought, was knocked down and continues to operate as a car park, while other car parks have replaced the former St John's market on Topping Street, and properties demolished on Leopold Grove and Cookson Street.
A new multi storey car park is also being built as the enabling phase of the £300m Blackpool Central Development.
The application will be considered by town hall planners at a future date.