Yes. You can be on annual leave whilst furloughed and it will not affect your furloughed status.  There may be a clause in your contract that allows the employer to ask you to take or not take holidays at a certain time so they may rely on this to ask you to take some holidays.  


Employers are asking employees to do this so that when things do return to normal, they don’t end up in a situation where everyone wants to take holidays, at a time where the business needs to increase trade and income. 


Even if there is no such clause in your contract, at law, an employer can force an employee to use annual leave as long as they give twice as much notice as the amount of annual leave they want the employee to use.  For example, if an employer wants you to take 1 week’s holiday, they would have to give you 2 weeks’ notice.  If they wanted you to take 2 days’ holiday, they would need to give you 4 days’ notice etc.