Like Brian I must point out that HMO's have a place in providing accommodation and are most often of benefit.
An application to convert a property to an HMO is very common with agreement or otherwise given by the planning office. Government, other than through the primary legislation (Housing Act 2004), has no part in the process so a petition is futile.
The only way to object is via the Planning Office for the Local authority when an application is advertised.
BUT it is possible, even probable that some may be planned to house those of which one disapproves in which case be careful to have actual evidence not rumour if placing an objection .