Can both parents have a period back at work at the same time, before taking further periods of shared parental leave?

Yes, under the shared parental leave rules, both parents can be back at work at the same time and still retain the right to take further periods of shared parental leave. It is not the case that one parent has to remain on leave.

Shared parental leave is aimed at giving parents more flexibility over how they share childcare between them during the first year of their child's life. The leave does not have to be taken in one continuous block; one or both parents can return to work and then take a further period of shared parental leave, provided that they comply with the notice requirements. The parents could decide to arrange alternative childcare and both return to work for a period at the same time.