The wire from the alternator to the starter solenoid (that's the 'common' connection on the Series III) should be at least 10 gauge. Brown insulation keeps it book color-code correct. Make sure all contacts are shiny bright.
The Lucas 16ACR alternator puts out 37 amps on its best day. You can upgrade to a Lucas 18ACR (fits earlier Jags) and not change a thing, 'cept getting 45 amps.
Which isn't much, considering that the Delco 10si is rated at about 90 amps. Several times I have tried to fit one of these, but using the stock location, it fouls on something or other (motor mount, engine block) as the Delco unit is larger in diameter than the Lucas one.
Robert Davis has developed a relocation kit that moves the alternator up a bit, to keep it high(er) and dry(er) if you do a lot of fording. The Delco 10si is about as big as you can go without going to a double-pulley set-up.
Cheers