I think this should do, a rent protected by statute.

UK law is very specific on rent control.

See below:

Protected tenancies are also called regulated rent act or fair rent tenancies. Their tenancies are regulated by the Rent Act 1977. Protected tenants are afforded protection from illegal eviction under the Protection from Eviction Act 1977.

To be a protected tenant you must meet the following conditions:

The tenancy must have commenced before 15 January 1989 and
The landlord is non-resident and
The landlord is a private individual or company
After 15 January 1989 no new protected tenancies can be created. There are some exceptions but these are limited to existing tenants moving to a new property provided by the same landlord under very specific circumstances.

For a tenancy to be protected the tenant(s) must have exclusive possession of at least one room but does not always have to occupy the property as his/her only or principal home - there are complicated rules about this.

Protected tenancy rents are called fair rents. This means they are not subject to market forces and are determined by the Rent Office.

There is probably a better way to say it in the context of the text e.g. a "decree" apartment. This suppose that there is a law (termed decrees in Italy, legislative decree, presidential decree, ministerial decree etc) which regulates these types of apartment. Where the reference is to a specific law in Italy I usually translate with the literal decree, rather than Act or Law or Ministerial regulation as the case may be.

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Note added at 39 mins (2006-10-05 11:34:34 GMT)
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If it is the Czech republic, then decree would be misleading and obscure, unless of course they have something very very similar to 'decrees' in czech language and law.