No.  You can only be furloughed or continuing to work.  Employers can furlough part time staff; staff with irregular hours or zero hours staff as well as full time workers. But you cannot work at all for your employer if you have been furloughed. 

Your employer cannot ask you to do any work while you are on furlough even if your employer is paying you the ‘top-up’ of 20%.  You can, however, continue with any training you are required to do for your job or book onto ad hoc training course provided by your employer.  It also appears that you are able to forward work to other colleagues who are still working to be actioned such as emails or sales leads.