Ok, you're on the right track. You know it sounds gritty and it looks gritty, therefore it IS gritty. Grit has to be removed. First so you can see if there is real damage, rather than just dirt, and second so the grit is gone and will not create more damage.

First step is to count the number of balls on each side and write that down. They are probably the same size on each side, and the same number. Clean all the parts with a solvent or Simple Green degreaser to remove all the old grease and the grit. There may be some scrubbing or hard rubbing with a clean rag involved. I think you cleaned out and repacked wheel bearings for those Mombikes, right? This is the same thing only bigger. The drive side cup will probably not come out in a patient time frame, so it's ok to clean it by reaching your fingers in and wiping. You should also wipe out the inside of the BB shell as well as possible. There might be a sleeve in there that protects teh bearings from crud that may fall in from another frame tube.

Ok, now that the balls, spindle, and cups ar eall clean and shiny, measure the diameter of the balls so you know what size to buy at teh LBS or teh LHS (local hardware store).

Take out a magnifying glass and look close at the surfaces where the balls contact the cups and the spindles.

There should be either no wear track (if your karma is perfect) or a smooth path where the balls have tromped through the years.

A rough track might be a problem, and a series of evenly-spaced deep divots IS a problem.

Another assessment to make is to take a ball-point pen and run the point along this track and next to the track to feel the difference between used and never-used. It will also let you feel the presence of wear. Any flaking of the hard finished surface is bad.

Check the fixed cup these same ways, it's just harder to reach it and feel it.

Flaked, divoted, or excessively-worn parts (cups or spindles) should be replaced, unless you can find someone who can be trusted and has a way to resurface and re-harden the parts. NOW you can speak intelligently about what needs to be replaced and what does not.

Buy new bearing balls. There's a lengthy debate possible about what grade, but I tend ot prefer Grade 100 for general purpose. I sprang for Grade 25 for the original Campy BB on my Masi, and it came out very smooth. I don't know what Raleigh or the other Brit companies specified for three-speeds.

Picking grease is a similarly contentious issue. I tend to prefer Phil's over old Pedro's, just because Phil's has a reputation of excluding moisture. I have not done a full study of grease, I'm sure there will be a debate.

I don't know if you should use threadlock (blue) or not for this kind of bike, but a little grease or at least oil on the BB threads would be a good idea, if you have wiped them down as well as possible. Some rinse inside would not be a bad idea, at least wipe with a solvent-dipped rag or q-tips.

I grease the drive side cup kind heavily and the drive side of the spindle, and place the original nummber of balls around the cup into the grease. Then insert the spindle into the BB and the end through the hole in the cup, being careful not to knock any balls loose. It should seat smoothly and you should be able to turn it when is home and enjoy the feeling of a smooth bearing turning. If it doesn't feel good, something might be wrong, so there's no problem with gingerly removing, inspecting, and re-assembling. After a try or two you'll see how it all works.

Grease the non-drive cup and spindle bearing surface, put balls into the cup, and just as carefully lead the cup up onto the spindle. When the cup wants to be threaded into the BB, do it gently so as to feel if there are any obstructions in the threads and to ensure no cross-threading. When it stops solid you have both bearings in contact, and sit back and feel the smooth joy of fresh bearings. Once you get it adjusted and lock-nutted correctly, it should be good for another few years if not 50. But after this one should really be overhauling the BB on general principles to eliminate the chances of grit damage.

Bearing adjustment is just like hubs. When the locknut or lockring is tight, it should be just tight enough that it has no rock or wiggle, but spins smoothly and freely. This setting is safe, in terms of proper support for the spindle and rigid positioning, and allowing maximum free spinning. It is definitely possible to complete this step better than the factory did.

When you get the drive and non-drive crank arms back on and secured, spend 10 minutes enjoying the flywheel effect.