Emergency services attended the scene at the Wood Street car park opposite Lancaster bus station on Tuesday evening.
The wall is on the side of the Eggcup foodbank charity building in Chapel Street.
Fortunately no one was injured in the incident.
Julie Seaton, CEO of Melbourne Food Club, said people whop would normally use Eggcup are welcome at other food clubs in the area if necessary.
"Gladly no one has been injured, so that’s a blessing,” she said on Facebook.
"Eggcup is just one of 13 foodclubs within the area. So if you are a member of Eggcup, can I just say as trustee of Lancaster District Food Justice Partnership that any of their members can be at ease with the knowledge that they are welcome at any other food clubs within the area.”
A city council spokesperson said: “Lancaster City Council is continuing to respond to the partial collapse of a property at Chapel Street/Wood Street, Lancaster.
“We were alerted to the incident during the evening of March 24 and immediately enacted our emergency procedures. Council officers attended the site, supporting our emergency service colleagues. The area was cordoned off, and the owner of the building was notified.
“An initial structural assessment was undertaken last night, and officers are attending the site again today (March 25) to make a secondary inspection during daylight hours, to assess the extent of remedial work that will be required.
“The main priority is to prevent any further deterioration of the building, and public safety will remain paramount.
“No entry to the building is permitted and the site remains closed off.”
Thanks to Andrew Reilly for use of his photos.
The incident follows the partial collapse of a wall earlier this month in Thurnham Street.
Several roads had to be closed off after the wall collapsed on the side of the Kwik Fit car park, partially crushing a car in the garage car park.
