"Stiff hill climbing without ropes and no real danger" is called via ferrata. In Germany and Austria is's klettersteig.
Unfortunately UK have only 3 routes and they are purpose built commercial attractions.
On the continent where are thousands of routes and they are public. Many are easy accessible and can be done in one day, others would take a hike to approach and few days to complete. Alps are probably the best place to go. With Dolomites and Tyrol being best places in Alps. However it's just my personal preference.
It's same scrambling or easy climbing, but with additional holds, sometimes ladders and bridges on lower grades. Plus you are clipped and falls extremely unlikely to be fatal. No ropes are needed, but harness, two slings and karabiners are bare minimum. Helmet and special lanyard instead of slings are advisable. Leather gloves are a good thing to have as well. No training is needed, just make sure at least one of karabiners is clipped to a cable at any given time.
You can always hold to cable and that really helps with balance. And it's best route to advance from hill walking in my opinion. Both safe, adventurous and usually very spectacular.
Post edited at 10:50