The "law" actually states very little. It cites the addition of Part P to the list of building regs and some other minor modifications to do with electricity in dwellings. It makes no mention of RCDs at all.
Part P of the building regs is also a little circumspect since it does not call up BS7671 as a mandatory set of rules to follow, but simply states that :
"0.2 A way of satisfying the fundamental principles would be to follow:
a. the technical rules described in the body of BS 7671:2001 as amended or in an equivalent standard approved by a member of the EEA; and b. guidance given in installation manuals that are consistent with BS
7671:2001, such as: i. the EE (Institution of Electrical Engineers) On-Site Guide; ii. the series of IEE Publications, Guidance Notes Nos 1 to 7."So the basic principle established is that you will comply with the building regs (and hence the legal requirements) if you follow BS7671. That does not prevent you complying with them by following an alternative standard of equal standing - although its questionable if there actually is one.
So if you accept that the baseline for any work will be BS7671 (aka "the wiring regs"), then you need to see if they (and their supporting documents) permit and installation with only one RCD. The answer to which, is they can; but only in very limited and unlikely circumstances.
For example a dwelling with a TN supply, and all lighting circuits etc wired with cabling protected by an earthed metal shield or at >50mm depth, could be run from MCB(s) connected directly to the main switch (i.e. traditional 16th edition TN style). All sockets circuits, and all circuits present in rooms containing a bath or shower could then go on a single shared 30mA trip RCD. A small flat or bedsit might conceivably be setup like this.
However, the cost of cabling in that way will far exceed the cost of adding a 17th edition style dual RCD CU - so in practice is unlikely unless its a really cheap job with all surface wiring.
So in the real world, two or more RCDs is mandatory, since a 15th edition style "whole house" RCD would not satisfy:
314.1 (i), or (iii), or (iv) 314.2and from the OSG:
3.6.2