There's a post on the GDS blog that might be worthy of your attention. It's from the boss - about 'digital transformation'. It's good.
It gets at a point I've being trying to articulate for a while - digital transformation is about making services better for everyone, not just people who use the website. (These are a couple of slides I've been trying out)
Everyone who uses government services is a recipient, and sometimes a victim, of government technology choices. Whether you're using the phone, or seeing someone in person, somewhere in that process will be an ancient clunky system making your life harder by making life harder for the people trying to help you. Digital transformation should fix that, not just fix the website.
Very often the digital bit in 'digital transformation' isn't the most important element - it just creates the opportunity for rethinking and redesigning the service, from the ground up, around the user. That's the important bit. And that's not just true for government.