I have a radial circuit protected by a 15A RCD at the consumer box for the immersion heater.
Firstly you seem to be confusing MCBs and RCBs. A RCD provides protection against faults to earth even very small ones but won't protect against overloads or other faults from live to neutral. A MCB provides overcurrent/short circuit protection. I'm guessing what you reffer to as a "15A RCD" is actually a MCB (post pics if you are still unsure and want a postitive identification). There is also a device called a RCBO that combines the functions of a MCB and a RCD.
There is a spur with a 3A FCU leading from it to the downstairs boiler and another one for the shower pump. Is this acceptable?
Afaict the OSG recommends that immersion heaters are on their own circuit but I don't belive there is a reg that actually requires this (please correct me if i'm wrong). IMO what you have is ok in that regard.
I want to run another spur/socket from the radial circuit; is this acceptable?
There are a couple of potential problems with adding a socket to this circuit.
The first is you need to consider the overall loading on the circuit. a 3KW immersion heater plus a couple of small loads will basically have the circuit maxed out. So by adding another socket you create a significant chance of overloading. While MCBs will protect against overloading to some extent it's still something you should avoid happening in the first place whereever possible. Assuming the cable is 2.5mm, not excessively long and kept away from thermal insulation you can probablly increase the MCB to 20A but even then it could still be overloaded if someone plugs an electric heater into the new socket.
The second is RCD protection. The 17th edition requires RCD protection for most sockets and for most concealed cables (both of these rules have exceptions but I don't think they are particually relavent here). How to apply this to existing installations that were installed to the 16th edition or before is somewhat debatable but the general consensus seems to be that any new wiring and accessories should be complient with the 17th edition and any existing wiring should be no less compliant with it than they were before. It is likely that your immersion circuit is not RCD protected (post pictures of your consumer unit and we can probablly work it out).
I have read so many times that you cant run a spur from a spur.
This statement is true but a little misleading. The thing is people say you can't spur from a spur but fail to clearly define what a spur actually is.
Afaict up to and including the 16th edition the term spur was only defined in the context of a ring circuit. In a ring the cable is rated lower than the breaker but this is considered ok as the current has two routes to get back to the origin of the circuit. In a spur there is only one route so if too much was placed on one spur the spur cable could be overloaded without tripping any breakers. Older versions of the regs used to allow one single or two double sockets on a spur but two singles was dissalowed (not sure which edition dissallowed it) because people were replacing single sockets with doubles without realising they were dealing with a spur.
The 17th edition also defines spurs in the context of radials but it only counts as a spur if it is of a reduced current carrying capacity compared to the main cable of the radial circuit.
In either cable a branch from a radial circuit in cable that is rated to take the full current of the circuit is NOT a spur.