I think everyone is being more than a bit harsh here, but at the same time, I don't generally disagree with anyone.
The OP is understandably frustrated.
The problem is that, as SimonG has said in post 25, we are being dripfed information. Whether the boiler was legally or illegally installed is not necessarily relevant to the radiator upgrade issue which is what we were originally asked to comment on, but let me give my ha'p'orth. Essentially, if a RGI has looked at the installation, said it was a bit rough but switched it back on (rather than note the system is At Risk or Immediately Dangerous), then the RGI obviously felt it was safe to do so.
There is, of course, a minefield of legalislation pertinent to the original installation being not installed by a RGI, and while we could give advice as to how you should proceed if you want to give us, clearly and concisely, the full details in chronological order of what happened, you have, instead, been trying to get us on your side. In practice, there are plenty of gas-safe installers that work alongside unqualified personnel. While the spirit of the law is that the work will always be overseen at every stage, the law is an bum in that, clearly the RGI will not always be in the same room as they are. So while you may be right that the RGI should not be sodding off early, you'd be equally right that the apprentice should probably stop work while the RGI goes to the toilet. But how can we possibly help if neither the HSE and Gas Safe does not plan to prosecute? It's not going to help a court case if some bloke on a web-forum (that you have previously dismissed as a keyboard-warrior) thinks your friend's installer is a cowboy. By all means instigate civil proceedings if you think you can win, and I, genuinely, wish you both all the best with this.
Reverting to the title question of October, what if you'd called me out to change the radiators (or what would a responsible workman do in this situation)? I would have made you aware that my quoted price related to fitting the new radiators and getting the system running but that I could not guarantee the new radiators would receive sufficient flow as I was connecting to existing pipe work. But then I have worked in a contracts office and have some experience with the wording of £100,000+ contracts so perhaps I cover myself more than is strictly necessary and I'm aware I may lose work out of this. Realistically, however, if the job was to change two radiators then your friend cannot expect a pipework upgrade if that proves necessary.
I think, if the radiators were 'only slightly warm' (and I can't know what that means as this is presumably you recounting to us what your friend - who is not a plumber - has told you) then I would also have turned off the other radiators and seen what happened. This would hopefully clear airlocks and restore flow, but would, temporarily, have the same effect as balancing the system, so we know that balancing and bleeding are not enough. Obviously I would not be able to balance the system if the new radiators are not heating through, so if there is not a problem with the goods supplied and fitted that day, there would now need to be a discussion: what does the customer want done? If the customer does not want to pay any extra, then I too would, reluctantly, leave the job like that. It does, however, sound strange that, however bad the pipework, the new radiators do not work fully when the other radiators are isolated and I, personally, would want to investigate. In the nicest possible way, however, I do ask myself, could it be that your friend may have approached the matter with the attitude that the plumber is " talking cr@p and its his job to leave the job with the new radiators red hot"? Because I have a lot of time for people, but faced with a customer who views me in that way, I too would be reluctant to return to site.