The police are not usually allowed to inform anyone of the fact that a person has been detained without their express permission.
When someone is arrested and brought to a police station, providing they are able to understand, they will be asked if they wish to have someone informed of their arrest. If they do not wish to have someone informed of their arrest the police will not normally go against their wishes. Usually the detained person will be able to make a telephone call to someone that they wish to speak to once they have been processed on arrival at the police station.
There are some exceptions to this, where the person who has been arrested is under 18 years of age we are obliged to contact a parent or guardian (which may include a carer or someone responsible for their welfare in certain cases). Also if the person appears to be unwell or in need of medical attention we may also contact someone who can provide further information about their medical history or ongoing medication so that their medical needs are properly met whilst in custody.
The final exception is where a senior officer has decided that it is in the best interests of the investigation to prevent the person having someone informed of their arrest or making a telephone call. This decision is not taken lightly and is fully documented with the reasons why, the police cannot hold a person incommunicado indefinitely and this officer will usually place a time limit on this to allow officers reasonable time to gather evidence but also allow the person to contact people who might be concerned about them within a reasonable timescale.
If someone who is in custody does want you to be informed of their arrest the custody staff will not give you information about how the police are progressing with their investigation.