By default you won't be able to ship with DHL Parcel UK on a bank holiday, the collection would be pushed to the next available working day instead. You can, however, get in contact with your DHL Parcel UK account manager and ask them to enable the deferred api on your account.
Once this is enabled you'll be able to ship with DHL Parcel UK on bank holidays with domestic bagit/parcel services. You will not be able to ship with international bagit/parcel services and ship on bank holidays
If you have any questions about this, contact support and we'd be happy to help!