The heart of the problem...
...is a bunch of un-elected, un-accountable civil servants who, with some (mis)direction from BIS, have chosen which laws they will enforce and which laws they will ignore. Ofcom's model of operation has been to generate cash for the exchequer and sod-all who get in its way!
Let us take the case of Electro Magnetic Compatibility. It is law, written into UK statute from EU Directive 2004/108/EC. The EMC regs were created in a time (1980s) when all sorts of electronic devices were bursting on to the market - and they were interfering with each other. EMC regulations set limits for generation of interference (some is allowed) and immunity from interference (your computer doesn't crash when you turn on a light). These are neatly rounded off with the essential requirements that devices do not wipe out important services, such as radio.
Add to the above, CE testing and certification. If a product is to be placed on the EU market, it must pass standardised tests to ensure CE compliance; and some of these include EMC tests for electronic devices. Member states are required to provide a Market Surveillance facility where products are monitored, and where necessary, tested for compliance. In the UK, that responsibility is handed down from BIS to Ofcom. So if you report a faulty electronic device to Trading Standards, they are supposed to be able to call on Ofcom's "expertise" to determine if the device meets the essential requirements of the EMC directive.
So why is the country in such a mess and the radio spectrum polluted with non-EMC compliant Power Line Technology (PLT), plasma TVs, switch-mode power supplies, and CFLs (to name a few)? Well, the buck stops at Ofcom. In cases where Trading Standards have sought help, Ofcom have said it's all OK and no laws are being broken, so TS cannot act. In a case where a computer SMPS was reported to TS, they could only act on the Low Voltage Directive and the supplier could only be warned. Had Ofcom used their legal EMC powers, the supplier would have faced court!
If Ofcom had acted correctly over the past 10 years, Power Line Technology would never had left the lab, as it cannot pass the essential requirements unless it is turned off; Panasonic would not be in radio-users' cross hairs over their Viera range of radio-noisy plasma televisions; cheap and nasty switched-mode power-supplies supplied without filtering components would be caught and their suppliers and manufacturers fined; and we would not be calling for Ofcom to be scrapped.
It should be noted that the RSGB cannot take over interference investigation or EMC compliance enforcement as they are not a legally bound entity. There is however, nothing stopping the current government from carrying out their pledge to remove Ofcom, returns its regulatory function to DMCS, and create a new organisation tasked with [radio] spectrum management and EMC compliance. The fines levied on all of the non-compliant manufacturers should fund the organisation for some years!