These offences took place between Thursday, September 24, and Tuesday, September 29.
In a statement the police said: "We'd like to speak to anyone who has a shed on the allotments and has had their shed broken into or damaged and has not reported it to us too."
Anyone who can assist the enquiry is asked to email [email protected], putting the reference 20000512540 in the subject box.
Alternatively call police on 101, quoting reference 20000512540, or the the independent charity Crimestoppers anonymously on 0800 555 111. You can also visit crimestoppers-uk.org.