With regard to the approach ban concept in the UK, I believe the relevant paragraph is CAP 393, Section 1, Part V, para 39:
An aircraft to which article 31 of this Order applies, when making a descent to an aerodrome, shall not descend from a height of 1000 ft or more above the aerodrome to a height less than 1000 ft above the aerodrome if the relevant runway visual range at the aerodrome is at the time less than the specified minimum for landing.
Article 31 refers to public transport aircraft.
This is nearly parallel to the US requirement for air carrier operations, contained in FAR 121.651:
b) Except as provided in paragraph (d) of this section, no pilot may continue an approach past the final approach fix, or where a final approach fix is not used, begin the final approach segment of an instrument approach procedure—
(2) At airports within the United States and its territories or at U.S. military airports, unless the latest weather report for that airport issued by the U.S. National Weather Service, a source approved by that Service, or a source approved by the Administrator, reports the visibility to be equal to or more than the visibility minimums prescribed for that procedure.
(c) If a pilot has begun the final approach segment of an instrument approach procedure in accordance with paragraph (b) of this section, and after that receives a later weather report indicating below-minimum conditions, the pilot may continue the approach to DA/DH or MDA. Upon reaching DA/DH or at MDA, and at any time before the missed approach point, the pilot may continue the approach below DA/DH or MDA if either the requirements of §91.175(l) of this chapter, or the following requirements are met: etc., etc.
The principal difference is the location, 1000 feet vs. the final approach point, etc. As has already been stated, Part 91 operations are rather less restrictive.
Regarding CAT III RVR requirements, Dbate cited Ops Specs para C060(d)(4), which addresses fail-operational landing systems with fail-operational rollout systems. Similar requirements will appear in C060(d)(3), addressing fail-operational landing systems with fail-passive rollout guidance. The important point in this configuration is that you will be using an alert height, not a decision height. Since no visual references are required prior to touchdown, there is no absolute need for touchdown zone RVR. This allows the TDZ RVR to be "temporarily" inoperative. However, temporarily generally does not mean deferred while waiting for backordered parts.
Para C060(d)(2) refers to a fail-passive system with any rollout system, and C060(d)(1) refers to a fail-passive system with no rollout system. The RVR requirements for a fail-passive configuration will always specify TDZ RVR because visual references are required in this case. The MID and R/O criteria are designed to address the rollout, with or without automatic rollout guidance.
Hope that helps a bit.