The joy of owning an LBC (Little British Car). Getting past the Queen's English, it's pretty straight forward.
The '70 has a tube axle, which, if you have experience with later model US made cars, it is very similar.
After you remove the road wheels and tyres (tires - ha, ha) and brakes (and yes, you need to disconnect the hydraulic line and remove the wheel cylinders to prevent breaking off the lines), you then need to remove the 4 bolts holding the backing plate and bearing to the axle housing. Access to those is through the hole on the stud ring at the end of the shafts.
Being a tube axle, the shaft is a swedge or press fit, so really no need to even open the differential cover (though there is another item that should be checked that I'll come back to later). Bearings are press-fit to the axle as well.
The hub will have to be removed. The cotter pin removed, the castleated nut may be easier loosened with the wheels on and even with the car on the ground.
The hub itself may take some doing to get off with a gear puller. I've sometimes had to apply heat along with some gentle persuasion.
Again, that can also all be turned over to the machine shop once the half shaft is removed. The best way to extract the axle and bearing is with a slide hammer attached to the lug nut studs (see sketch below.)
There are plenty of YouTube posts on this as well. They're for American cars, but the assembly is very much the same.
Once the shafts are out, use a press to change the bearings or give them over to a shop to do. Be sure to get the bearing kit (Moss part #125-850; 2 required) as it will have the seals needed with the bearings. You might also want to get new collars and spacers just in case.
Installation is just the reverse of removal, with the last part being a light hit with a soft blow hammer to the end of the shaft to seat it.
Now, inside the differential are (2) thrust washers, which, when new, were made of a fiberous material and are notorious for wearing, cracking and falling out causing a noticeable "click" when you accelerate and decelerate. Replacements are now bronze and more durable. Installation requires removing both half shafts (which you are doing anyway) and taking out the diff to bench work it. Still a bigger job than just the bearings, but if you need them, now's the opportunity to do this work.
I hope that helps you. Let me know if you have any questions and how you make out.
Safety Fast!
Art