A consortium that included Llewellyn was appointed preferred bidder for the scheme in late 2001. It is believed that Llewellyn's decision to withdraw was a consequence of its acquisition by Rok, the West Country contractor that bought Llewellyn for £16.2m last summer.
Sources on the team said Llewellyn had been struggling to get the project off the ground because of difficulties with the price.
Boxwood, the special purpose vehicle set up by developer Parkwood to manage the deal, said the project did not fit Llewellyn's new business strategy.
Project director Mark Davies said Boxwood was working with Gleeson elsewhere and that it was "very happy to have them working with us on Bexley. They have a strong track record with local authority leisure centre projects".
Financial close is expected some time in March, and construction will start in the summer.
Llewellyn was struggling because of difficulties with the price
The development is a mix of refurbishment and new build. It involves the upgrading of council leisure centres in Lamorbey, Riverside, Splashworld, Crook Log and Erith. The first three will be demolished, Crook Log and Erith will be refurbished and substantially rebuilt, and a new centre will be built on a site in Sidcup, subject to planning approval.
The scheme was designed by LA Architects and M&E consultant Max Fordham, and is being funded by Sport England and Bexley council. It is one of the first PFI projects that Sport England has funded, and is the largest leisure PFI project in the UK.
Parkwood has teamed up with Barclays European Infrastructure Fund to set up a firm called Leisure Plan. This will pay for £200m of leisure PFI projects over the next five years. Parkwood is expecting Bexley to have an annual turnover of £5m.
The Bexley scheme is expected to be Parkwood's second leisure PFI scheme to reach financial close. The developer has been named preferred bidder on four of the five leisure PFIs so far announced.
One of these, a £6m scheme in Sefton, Merseyside, is the first in the UK, and is due to open this month.