Eric Wright Construction is building the Animate complex on behalf of sister company Maple Grove Developments and Preston City Council.
It will have will have an eight-screen cinema, a 16-lane bowling alley, five restaurants and bars and an underground car park.
Works include improved pedestrian access between Animate and the bus station, as part of a wider £200m Harris Quarter public realm and lighting scheme.
Construction costs have already risen from £40m three months ago to £45m today.
Maple Grove director Andrew Dewhurst said: “There are now nearly two years of construction work ahead of us on the site of the former markets but the benefits Animate will bring to Preston once it is open will make it certainly worth the wait.”
Eric Wright Group managing director Jeremy Hartley said: “As a local business with a long-standing history of supporting improvement to our northwest towns and communities we are very proud to now be in a position to deliver this leisure-led scheme for the people of Preston to use and enjoy.”
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