The Liberal Democrat MP said he planned to contact other MPs and local authorities to find out whether they had received complaints.
Countering the concerns, Connaught said that since the contract started in April: "We have seen significant improvements and received feedback that the service is now better than it was before the letting of the current contract."
A Norwich City Council spokesman said: "As far as the council is concerned, Connaught is still fulfilling its contractual obligations - bins are still being emptied, grass is still being cut and housing repairs are being carried out."
The MP's campaign is the latest blow to the company, which has issued three profit warnings since June, damaging its share price.
In response to reports that rival companies Mears and Rok were eyeing up its customers, a Connaught representative said: "Clients are currently checking their contingency plans - every local authority has one. Customers are understandably checking that it's all robust."