If you have an early B, with positive ground, change the charging system to negative ground.
Change all charging systems to a high-output GM alternator and add an additional heavy gauge brown wire to the battery terminal on the solenoid.
Replace any “repair”-type battery terminals with either sweat-on or crimp-on bronze terminals. Clean main ground points and add contact grease before tightening again.
If your car came with twin 6v batteries, switch to a single group 26 12v battery in the right side well. Some batteries come with a small molded flange at the bottom, which can interfere and make for a very tight fit. It can easily be cut off with a hobby knife or grinder. You can put a plastic box insert in the driver’s battery well and use it for spares parts or whatnot.
Change to electronic ignition. Either a Pertronix, Lumenition or Crane unit fitted into a point distiributor. One of the later CEI Distributors is perfectly acceptable. An OPUS distributor should be replaced with a different system, before it drops dead and leaves you stranded.
If you opt to keep your Lucas distributor, do take the time to pull it out and send it to Jeff Schlemmer at Advanced Distributors. He will rebuild it, re-bush it as required, and make sure the curve is right for your engine and driving style, rather than what the dips at British Leyland came up with that week. And for a very fair price, I will add.
A third distributor option is Marcel Chichak’s 123 Ignition. This solid-state distributor has 16 built-in advance curves, no mechanical advance mechanisms to wear out and uses the most excellent Bosch 4-cylinder caps and rotors available anywhere.
Add relays to the horn, headlamp circuits, both high and low, and to the fan blower circuit. Run the feeds to the main brown union, and either use an inline fuse for each relay or add a separate fuse block to supply the upgraded circuits with the supply to main battery lug on starter.
Fit H4 headlamps with bright white bulbs. These are a simple bolt-in item. The pattern is far superior to a regular round headlamp and the replaceable bulbs are available in many output ratings and in several colors. A 55/65 bulb will draw no more power than a stock headlamp, but put out far more useful light. If the headlamp circuit is set up with relays, brighter bulbs can be fitted, up to 80/100. At this output, aiming is very important, so as not to dazzle oncoming traffic. (Check local laws for acceptability of brighter bulbs. New cars come with frighteningly bright headlights, and our old round lamps are but a drop in the bucket in comparison, so it should not matter. Still, its best to keep the local gendarmerie off of your back.)
Fit LED bulbs for the interior courtesy lamps. These can put out either slightly less light than the regular festoon bulbs, all the way up to vastly more light, but they do not make any heat to speak of and will not drain the battery of a door is left ajar.
LED tail light bulbs. Not the ones sold at swap meets with a bunch of LEDs in a housing, but the 3W or 5W Luxeon ones with a single LED. These things are rather expensive, but they put out much more light than the regular incandescent bulbs. Aything that makes these cars more visible is a good thing. You can also use the "tower" style of multiple LED bulbs, but the cost on these is about the same as the Luxeons.
Fit a solid state flasher unit instead of the original thermal one. These go for around $14, will drive LED bulbs, and are a direct replacement. No more slow flashers in cold weather.