How would you do this safely (is this even possible to do safely)?
This technique is based on one member of the party being more competent than the others and the grades being very low (probably nothing more than a Grade III scramble)
For example I lead a group of friends up Tryfan. This is a grade I scramble. I took a rope. I was confident soloing any climbing sections (this is well below my climbing grade) and I used the rope to help the less experienced members.
I didn't use a "handline" (something for people to hold onto is of limited use as if someone falls it's not really going to help)
If there isn't a member of the party who is competent enough to solo the climb then your right, your into the realm of "technical" climbing.
Grade I or below
Most Grade I scrambles are within the range of anyone who is competent in the mountains. Above this you need more skills. If your not confident to lead a Grade I then your not confident to be doing this at all. Get some more experience then come back.
Grade II/III and climbing
This isn't totally inaccessible you just need take a bit of time to learn scrambling rope techniques, how to belay, etc. you can still do this. You will likely need some more kit and you will need to learn how to use it (i.e. harnesses and belay plates and some kind of protection such as nuts). Your local climbing wall is probably where you start with this, most have beginner courses that will teach your how to belay, etc. You then need to learn to place the gear and protect the climb. But scrambling is a really good place to learn to climb and improve your confidence. But learn the basics somewhere safe (indoors) first!
There are a series of British Mountaineering Council videos covering the subject in detail
at some points it mentions the idea of using a hand line on some more
exposed routes to give something to hold on to....Presumably, the most
able climber in the group would go forward and anchor a rope along the
route for other climbers in the party to use?
This isn't a technique I'm familiar with, plus I don't really see the benefit. If someone isn't confident they either shouldn't be there at all or should be properly secured for their safety. Couple of issues here:
- A rope is really unpleasant to hold.
- If you fall and hold the rope, expect serious burns.
- If you fall what are the chances of you catching the rope?
for that reason I'd prefer to use a different technique:
I used a figure of eight lasso(passed under the armpits of the person) to secure the people and I either belayed off spikes or hip belayed. The rope's main job was to give the person confidence, but in the unlikely event that they do fall, I could catch them without relaying on them holding onto something. If the pitches are quite long, then you probably want harnesses.
I'm wondering if you mean like on a via ferrata?

In this instance the line is secured to pitons hammered into the rock and is permanently fixed. Someone will of done this for you. You typically secure yourself using a cows tail or via ferrata kit.