1a) Before you cut anything off, measure EVERYTHING! brace the gap. I brace between the dash next to the screen pillar and the B (and c pillars if a 4-door) pillar. This is so the door can still be re-fitted to check the gap.
1b) Measure the distance from boxing plate to outer sill edge at the front and rear of the door aperture.
2) Drill out boxing panel spot welds and remove boxing panel, and using 1mm discs on grinder, cut off the floor edge panels and the sill outer edge panel.
3) You should not have just the inner sill step between the A and B pillars. A good opportunity to clean up and paint the inner sill step, or make good any repairs- using thicker gauge steel 1.8 or 2mm. Spray any areas to be overlapped with Zinc weld through spray.
4) First piece I would weld in is the boxing panel.
Punch or drill holes every inch in the top of the new sill boxing panel and plug weld this to the lip of the inner sill step. You can also punch holes in the lower lip of the boxing panel to enable plug welding to the rest of the sill. Apply zinc weld through spray (before welding) to any overlaps such as between the boxing panel and lip of the inner sill step.
4 1/2) Prepare the lower sill panels. Wipe with a cloth soaked in cellulose thinners. If the black paint comes off your panels have been painted in cheap shipping primer. Remove this and paint with decent primer (zinc weld through where panels are to be welded. At this point punch or drill holes ~ every inch on the inner flange of the outer sill panel to enable plug welding later on.
5) Then, once the boxing panel is in, tack weld the outer sill edge to it- tack it in with reference to the measurements taken in step (1b) and re-fit the sill covers and sill finisher channel, close the door to check that the sill finisher channel is flush with the lower edge of the door. There is also a large overlap on the floor edge panels to allow for adjustment of the sill and so the floor edge panel will meet the floor. Cut off most of this flat overlap, leaving a 1/2" lip. Punch/ drill holes in this lip to later enable plug welding to the floor. (some might argue that the edge should be lap welded to the floor. Again, apply zinc spray where the floor edge panel will overlap the floor.
6) The channel in the floor edge panel should be re-formed so it is a "squarer" profile and the lip can butt up better to the lower lip of the boxing panel and the inner lip of the Outer sill edge panel. (My interpretation of Jonothan's comments).
7) Fully weld in the outer sill panel to the boxing panel (plug welds and seam welds).
Plug/ seam weld floor edge sill panel to floor at the inside and sill outer panel/boxing panel on its outside. Also plug/ seam weld the sill outer edge panel to the A pillar.
8 1/2) This is a good time to fit the new jacking point at the end of the centre crossmember. A small rectangle of 2mm plate may be needed to be welded vertically so the jacking point and outer sill panels meet without any gaps.
9) Grind smooth any welds, prime (I use zinc primer), seam seal any seams and welds, paint (I use chassis black for the sills) - can also use stone chip paint on any areas that might be blasted by water and stones, such as the parts of the sill near the wheel arches. Then re-paint the stone chip paint with more chassis black. Finally, when dry, cavity wax can be applied inside the new sill structure and underbody wax outside the sill structure.
I like to save the inner sill step, if possible as this undoubtedly helps the car keep its shape, but when rust has appeared you generally need to replace all the rest of the sill panels for a decent job.
If the floor is also bad/rusty/cracked, fit all the rest of the sill pieces, except the floor edge sill panel, then fit new floors, weld them to the inner sill step and finally fit the floor edge/ sill panel. This order of assembly is necessary because the floor is sandwiched between the inner sill step and the floor edge panel.
A decent standard of welding is needed to effect these repairs. In particularly, one needs to be proficient at plug welding to ensure one makes strong plug welds.
I'm hoping Jonothan and any other decent professional reading this will jump in and make some suggestions/ corrections.
I have described the front part of the sill repair, the rear repairs are similar, except one has to cut the rear floor edge panel to butt up to any front spring hanger repair plates that may have been fitted.
I'm about to do this job on my 4-door, so I will write this up later in full, with pictures as a "Sills, How To Guide" on this forum, and possibly on t'other forum as well.
Who knows, "Morris Minor Restoration"- the book, film and stage play may soon follow