yes.
A valid driving licence with photo is acceptable photo ID for travel on domestic flights within the UK and domestic flights within the Republic of Ireland.
No: Ryanair.com - FAQS : What photo-Id do I need?
But I'd double check with whoever you're flying/sailing with.
Edit: Common Travel Area - Wikipedia, the free encyclopedia
to me - ROI is a DIFFERENT country to the UK and therefore passports would be required.