Residents have described their distress at recent incidents, one of which occurred on Saturday night and left debris including a bumper and part of a number plate scattered across the pavement at the top of Hollybush Road.
The crash, which is believed to have been caused by a white van at about 11pm, happened when a driver lost control of their vehicle and smashed through the wall past Rose Lane, near the roundabout joining Listley Street, St Mary's Street and the B4373.
Bricks and mortar fell onto the property of retired resident Paul Lewis, 76, who said had the culprit crashed "a few yards further down", he would have driven off a cliff.
Mr Lewis, who moved to Bridgnorth in 1984, said: "I'm living on my own here; it is a distressing incident but we've been having quite a lot of problems with speeding cars late at night, especially on the weekend.
"If they had crashed a few yards further down they would have plunged through the wall and over a sandstone cliff into my neighbours garden and would have been killed.
"The wall must be 170 years old, in a conservation area, and the last time it had any damage is from a German bomb in 1940 – it's about a 10ft stretch that's been destroyed.
"Somebody did witness a white van roaring out of Listley Street, missing the kerb and hurtling across the road before knocking the wall down – it must have then withdrawn itself and sped off."
Mr Lewis added that he had received "great support" from friends and neighbours, who cleared bricks and ensured the area was safe for him to live.
Marguerite Elcock, 53, former crown court prosecutor, has lived in the town for 30 years and said she expected more to be done by the police.
"I am sure that had this happened in Shrewsbury the police would have been more proactive," she said.
"Following Councillor Julia Buckley's intervention, a community support officer is going to look at town centre CCTV.
"This could be a theft, a dangerous driving, an incident of driving under the influence of drink or drugs – who knows – yet only after pushing from a councillor are the police interested.
"As a resident of Bridgnorth for 30 years I can honestly say that it feels very much as though Bridgnorth receives a second rate service from West Mercia Police."
A spokesman from Bridgnorth police said: "PCSOs Mandy Leek and Steve Breese are carrying out CCTV enquiries after considerable damage was done to a wall of a property not far from the mini-roundabout opposite the Listley Street junction on Hollybush Road."
Anyone with information should contact police on 101 or email firstname.lastname@example.org and quote incident reference number 00337_i of June 20.