The original brakes (calipre?) have a "short" cable pull. I'm thinking the mtb brake levers you put on were for v-brake style brakes which have a "long" cable pull (that's why they feel stiff -you have no mechanical leverage).
However.... if you can get hold of some older mtb brake levers that were intended to be used with canti brakes (short cable pull required), you should be OK. Otherwise, it's back to those original levers or replacement levers with a short cable pull. Even appropriate pull levers can be a crap shoot -cable pulls can still vary by millimeters and provide a surprizingly different feel to the brake (e.g. my Shimano STI levers pulled less than the Cane Creek replacments I got, even though they are meant for the same brake style).
I should also add you should consider at a minimum making sure your rims and pads are clean. If you can afford it, also try some KoolStop salmons or similar for the brake pads as well. You also mentioned its an old Raleigh; I don't know if you have single pivot or dual pivot brakes, but I've had better luck with dual pivots so try those if you haven't already or can afford them.