The Anthony Rhodes pdf entitled “Repairing Jaeger & Smiths Speedometers” repair is a very good read and this short few paragraphs is meant as a supplement to that.
1/ The hardest part is removing the needle from the front face of the speedo. I(f it has been wedged onto there for the last 45 years then it’ll take quite a lot to pull it off. If you can get past that stage without breaking anything then you are past the worst.
2/ The odometer and speedometer functions are almost completely separate and although it is mentioned, the easiest way to correct the speed is to find a spare speedo of the same basic construction and swap the rear cage with magnet over, lock stock and barrel.
3/ If the odometer misreads (e.g. because you have swapped out the differential) then there is no choice but to replace the worm gear/pinion gear combination. Even minor corrections have to be addressed this way as the odometer is a separate mechanical function related solely to the number of turns the speedo cable makes.
4/ Not mentioned in the article is the right angle drive at the gearbox end. These come in two varieties. For non overdrive boxes, the turns ratio is 1:1 and for overdrive boxes, the ratio is 11:14. I presume the different angle drive ratios reflect the use of an overdrive final gear on the gearbox and this arrangement also means that the turns per mile worm/pinion used in MOD saloon car speedos is a lower number than in speedometers for non overdrive cars.
5/ The article shows a picture of the magnet and drag cup assembly for the speed indication. Not mentioned, but visible is that the magnet has two trapezoidal “wings” spot welded to it. My guess these are for fine adjustment of the magnetic strength, as they can be bent to be closer to the drag cup and thus slightly increase the magnetic flux seen by the drag cup. This will make the speed read higher and I expect minor adjustments of a few percent can be effected by adjusting how closely the wings are bent to the drag cup. It also implies that another method of adjustment would be to alter the air gap between the drag cup and the magnet/rear cradle assembly by means of washers under the screws which separate the front and back halves of the works. This would have to be done subject to not altering the action of ratchet assembly for the odometer on the front half of the odometer assembly.
6/ The angle drives appear to have different length spigots, presumably because the mating assemblies in the tail of the basic gearbox are different from that at the end of the overdrive box. It is my view that the shorter stub from a BG2402/08 (11:14) meant for the overdrive box is slightly too short and a speedo failure may actually be simply that the spigot at the gearbox end has been rounded down a bit through wear. (I base this on swapping in a BG2402/07 1:1 and getting the speedo function back straight away, albeit with the wrong ratio now).
Rather than attempt to lengthen the short stub, one approach to correct this deficiency is simply to turn down the overdrive gearbox brass insert which threads into the overdrive tail that the angle drive connects to, shown as “C” in the above picture. (The angle drive knurled cylinder connects at c2 and thew c1 end screws into the gearbox tail. This shortens the distance between c1 to c2 and effectively makes the angle drive stub longer by the same amount. A flat sectioned spanner is needed to unscrew the insert (you can see one of the flats in the picture midway between c1 and c2 and behind the c1 end will be acopper sealing washer. Inside the assembly will be what looks like a thin brass olive, presumably part of the oil seal arrangement. Protruding out of gearbox will be a brass pipe which sits down the middle of brass insert “C” and this is limit of how much you can turn down the insert. You can take about 1mm off of the c1 end and about 3mm from the c2 end without altering the functionality of “C” and it makes the “a1” stub end about 3-4mm further inside the gearbox so it mates better and the spigot tip suffers less future wear. It also “fixes the speedo” in this case.
7/ The clearance between the tunnel and the angle drive is notoriously small and the etype angle drive “B” has its (grub) screw head “b2” broken off whereas “a2” is intact. This may not be a factory approved modification, but I suspect it was done to give an extra 3mm clearance between the angle drive and the tunnel. Non-contact means no kncking or vibration, means no lossenening of one against the other, means no unanticipated wear, means no premature failure.