For anyone who has watched House you'll know there is a continuous theme of the doctors breaking into patients homes to look for toxins and possible environmental causes for their illness. Their policy for not asking permission is that everyone lies and even when it comes to health people will sometimes hide relevant information like drugs or other possibly embarrassing things. If they argued that it was medically necessary and based on the fact that they do often find medically useful information; what would happen if someone, not liking what they did, reported it to the police?
They get a $550 fine
Entering a building without permission is an offence under s4 if the Inclosed Lands Protection Act 1901
In addition, they would face discipline from the Medical Board of Australia for ethical violations. Please refer to section 2 which requires them to “be honest, ethical and trustworthy.”
If the doctors do not damage the property and if they do not remove anything with intent to permanently deprive the owner of it, then they haven't committed any criminal offences. They have only committed trespass, a civil tort.
I seem to recall at least one episode of House in which the doctors ate snacks they found in the property. This is technically theft but I doubt anyone would be interested in reporting or punishing it.
"What would happen if the police found out?" - they might investigate but, having learned there was no crime, that would be the end of their formal involvement. They might informally admonish the doctors.
If the doctors do cause damage (Crown Prosecution Service guidance: criminal damage) or remove something (CPS guidance: Theft Act offences) then the police and CPS might be more interested.
If it came to the attention of the police that a doctor carried lockpicks then they might be investigated for Going equipped for stealing, etc to s25 Theft Act 1968.
It might be decided that a 'caution' (an out-of-court disposal) is appropriate, particularly for a first (known) offence. Cautions can appear on Disclosure and Barring Service (DBS) checks, which may affect the person's career in healthcare.
It might be decided that neither a caution nor a prosecution are in the public interest.
If the CPS decide to prosecute, in the context there is no statutory defence to criminal damage or theft/burglary (there is a 'lawful excuse' defence to criminal damage but it doesn't fit the context).
The defendant might try to argue a 'defence of necessity', i.e. the patient was near death and the defendant committed this relatively minor offence in an effort to save the patient's life. But it's likely this argument would have already been raised and seen as a reason not to prosecute.
The doctors should also be concerned about their status on the General Medical Council's medical register. They could lose their licence to practice in the UK. However, a theme of House was that the authorities tended to turn a blind eye or only issue relatively minor punishments (such as extra hours on dreaded clinic duty).
Most states in the USA include an unauthorized entry law.
Louisiana Revised Statute RS 14:62.3 - Unauthorized entry of an inhabited dwelling
New Jersey Revised Statute: Section 2A:39-1 - Unlawful entry prohibited.
Those doctors would be breaking the law and I'm guessing placing their medical license at serious risk doing this as part of their practice.
Understanding the law & general criminalization of almost everything in the USA, it's absurd to think it isn't against the law to go inside someone else's house.
It is not a crime to enter a house in California without prior permission from the owner, but it is trespassing to do so if the place is posted "No Trespassing", if told by the police to not enter, or if told by the owner to not enter or to leave. There are also intent-related restrictions for example enter with the intent to steal, destroy, obstructing lawful business, harvest shellfish and so on.