You don't understand the powers of arrest. Your a and b aren't the only reasons someone may be arrested. And yes you can have the record deleted if you haven't been charged/taken to court and don't have a previous record.
The police arrest for many reasons, they can as easily de arrest and more often than not they aren't made into official records. De arrest and released without charge are two different things.
In your hypothetical case, if you have been arrested for either reason, the arrest ( if you are arrested, you may just be asked to go to the station to help with enquiries) may not go as far as being noted other than in the officer's notebook, if ten minutes after you've been arrested the call comes over the radio that they have found the real suspect, you will be de arrested with no record of the arrest. The police don't have to prove beyond reasonable doubt, they don't actually have to 'prove' anything. They are investigators with any evidence being put into a file for the CPS so they can decide whether it's a watertight case, borderline or there's no evidence. the police can charge someone but it will the CPS who decide on whether it goes to court.
Other reasons to arrest.
(4)But the power of summary arrest conferred by subsection (1), (2) or (3) is exercisable only if the constable has reasonable grounds for believing that for any of the reasons mentioned in subsection (5) it is necessary to arrest the person in question.
(5)The reasons are—
(a)to enable the name of the person in question to be ascertained (in the case where the constable does not know, and cannot readily ascertain, the person's name, or has reasonable grounds for doubting whether a name given by the person as his name is his real name);
(b)correspondingly as regards the person's address;
(c)to prevent the person in question—
(i)causing physical injury to himself or any other person;
(ii)suffering physical injury;
(iii)causing loss of or damage to property;
(iv)committing an offence against public decency (subject to subsection (6)); or
(v)causing an unlawful obstruction of the highway;
(d)to protect a child or other vulnerable person from the person in question;
(e)to allow the prompt and effective investigation of the offence or of the conduct of the person in question;
(f)to prevent any prosecution for the offence from being hindered by the disappearance of the person in question.
(6)Subsection (5)(c)(iv) applies only where members of the public going about their normal business cannot reasonably be expected to avoid the person in question.]
consultation with the Director of Public Prosecutions ( that person doesn't actually do this, it's the CPS in their name)
Consultation with the Director of Public Prosecutions
F2dealt with under section 37(7)(a)] above, an officer involved in the investigation of the offence shall, as soon as is practicable, send to the Director of Public Prosecutions such information as may be specified in guidance under section 37A above.
(2)The Director of Public Prosecutions shall decide whether there is sufficient evidence to charge the person with an offence.
(3)If he decides that there is sufficient evidence to charge the person with an offence, he shall decide—
(a)whether or not the person should be charged and, if so, the offence with which he should be charged, and
(b)whether or not the person should be given a caution and, if so, the offence in respect of which he should be given a caution.
F3shall give notice] of his decision to an officer involved in the investigation of the offence.
F4(4A)Notice under subsection (4) above shall be in writing, but in the case of a person kept in police detention under section 37(7)(a) above it may be given orally in the first instance and confirmed in writing subsequently.]
(5)If his decision is—
(a)that there is not sufficient evidence to charge the person with an offence, or
(b)that there is sufficient evidence to charge the person with an offence but that the person should not be charged with an offence or given a caution in respect of an offence,
a custody officer shall give the person notice in writing that he is not to be prosecuted.
F5(5A)Subsection (5) does not prevent the prosecution of the person for an offence if new evidence comes to light after the notice was given.]
(6)If the decision of the Director of Public Prosecutions is that the person should be charged with an offence, or given a caution in respect of an offence, the person shall be charged or cautioned accordingly.
F6 (whether because of section 17 of the Criminal Justice and Courts Act 2015 or for any other reason) ] , he shall instead be charged with the offence.
(8)For the purposes of this section, a person is to be charged with an offence either—
F7(a)when he is in police detention at a police station (whether because he has returned to answer bail, because he is detained under section 37(7)(a) above or for some other reason), or]
(b)in accordance with section 29 of the Criminal Justice Act 2003.
