Government guidance tells us that once we are ‘on furlough’ we are unable to carry out work for our employer. We may be able to do training as long as it is not making money for, or providing services to, our employer. We can still work for another employer, if for example we have a second job, but any employer that puts us on ‘furlough’ can not request we undertake any paid work for the duration of the scheme.

For full guidance see here https://www.gov.uk/guidance/check-if-you-could-be-covered-by-the-coronavirus-job-retention-scheme#while-youre-on-furlough