My advice to employers dealing with staff involved in rioting were recently published by Sky News: 

It's correct for employers to be concerned about employees’ actions outside of work.  Rioting could call into question an employee’s character and/or likely to be contrary to an employer’s inclusive polices (especially given the nature of the current riots).  Such behaviour could also have adverse reputational consequences for businesses.

However, before dismissing an employee it’s important that an employer considers its own internal disciplinary procedures.  It’s important that matters are investigated and employees are given the opportunity to state their case (even if the evidence is clear).  Failure to do so could give rise to an unfair dismissal claim.  

This is also true where an employee has been arrested.  In most cases it would still be appropriate for an employer to carry out its own internal process, rather than simply relying on the fact he or she has been arrested (especially where an employee has only been criminally charged, rather than convicted).  The position is more complicated where an employee is remanded in custody and cannot attend the workplace - in those circumstances, it might be less risky for an employer to dismiss or argue that the employment relationship has ended due to "frustration" - because the employee is unable to perform their contract.