I've got one of the Edwin Jaggers, it's great, but I don't like the Derby blades, I use Red Personnas (same as Tesco own brand).
I think the main issue is not the razor but the preparation, washing your face with soap and really hot water first and/or using a hot flannel/towel like the barbers do makes a lot of difference, softening the beard.
Using a proper shaving soap or cream is also an improvement, Palmolive cream in a tube is still widely available and cheap. Taylors is great stuff, but Body Shop also sell the same cream and a reasonable cheap synthetic brush.
The razor is not so important, I've had the same or better results from a single blade Bic disposable as I get from a Gillette Fusion or whatever, provided I've done the prep above.