If someone commits tax evasion, will they be arrested by local police, or the IRS’s CI and Justice Department?
The IRS Criminal Investigation division is typically going to be the arresting agency, assuming that (1) the offense is treated as a criminal matter; (2) a warrant is actually issued; and (3) anyone actually sets out specifically to serve the warrant.
It is usually the case, though, that the violation is handled as a civil matter. When it is treated as a criminal violation, the defendant and the Service often reach an agreement that eliminates the need for an arrest. If there is a warrant, though, any police agency could theoretically make the arrest if they happened across the defendant. But if it's a time-sensitive investigation -- if the defendant is expected to flee or destroy evidence, for example -- it's a safer bet that you'll see an actual warrant execution. In that case, you would have CI taking the lead, perhaps with assistance from other agencies.
If someone commits tax evasion, what organization will arrest them?
First, not all tax evasion is dealt with as criminal conduct. The relevant authority, HMRC, can impose civil penalties instead - in the most severe cases this can amount to 100% of the tax due.
This may be, in no particular order:
Note that although the Serious Fraud Office can investigate and prosecute offences, its employees do not have the power to make an arrest.