There are two related questions:
- What factors determine how police will exercise their investigative discretion?
- How will charging decisions be made?
I cannot enumerate the multitude of factors that inform the police's investigative discretion, but this guide from the College of Policing is a good resource. At the initial stage, factors include: scene management, risk management, record keeping, community impact. The priorities are to: preserve life, preserve scenes, secure evidence, identify victims, and identify suspects. The initial investigation is aimed at dealing with the immediate needs of victims and witnesses and gathering enough information to allow an investigative evaluation.
Whether the investigation goes further depends on the circumstances of the crime, the material gathered so far, and resource requirements.
Eventually, the police will coordinate with Crown Prosecution Service to identify further investigative needs of the prosecution, if a charge has been laid or is being considered.
More specific steps are discussed here. Importantly:
Each force sets their own crime investigation standards, which are disseminated to staff. They should be interdependent with the national intelligence model, to ensure that they support the deployment of appropriate resources to areas of identified priority at the correct time.
Police officers exercise a high level of discretion when dealing with situations on the street. This is not directly overseen by sergeants and inspectors, and this makes the supervision of frontline officers challenging. Crime investigation standards are, therefore, useful to monitor and measure the performance of individual investigators and the quality of the investigation.
Here are two resources describing the charging decision:
The default is that in order to charge, prosecutors must be satified that there is sufficient evidence to provide a realistic prospect of conviction and that there are no public interest factors tending against prosecution which outweigh factors in favour of prosecution.
But, there are a limited range of cases in which the seriousness or circumstances of a case justify making an immediate charging decision, even though there is insufficient evidence to meet the "realistic prospect of conviction" standard. In order to charge in these special circumstances, five conditions must be met. I will not describe these in detail, but there must reasonable grounds to suspect that the person has committed the offence (this is a lower standard than a "realistic prospect of conviction"), there must be further evidence forthcoming, the seriousness of the case justifies making an immediate decision, there are substantial grounds to object to bail, and it is in the public interest to charge.
Further, there is a lot of discretion for police or prosecutors to proceed with an out-of-court disposal where it is in the public interest and is an appropriate response.