if its faulty within 6 months its classed as faulty from new and a consumer has the immediate option of a full refund from the seller..you. That is the bit your missing it would seem.
If you are talking about the right to reject under section 20 of the Consumer Rights Act, your interpretation is different from that of 'Which?' (formerly 'the Consumers' Association').
It would seem the 30 day period is unconditional (for supply of faulty goods, NOT SERVICES), and your point about assumption of faulty goods during the 6 months is correct, but does not give you an automatic right to a refund if, say, the hinge on the control panel cover breaks after 5 months.
Having skimmed through some of the leglislation itself, it is quite complex and a bit beyond speedy comprehensive understanding by myself because, while educated to a high level, I am not educated in law.
If a consumer could reject a boiler and require a full refund on it after 5 months after one failed repair, I suppose this situation could come about, but the refund would seem to be on that item not the entire installation so it's unlikely a customer would want this outcome. In this case, I'm sure the boiler manufacturer would help the installer else we'd all be hearing about it on this forum. You do make an interesting point about breakdown of costs - but I wonder how BOXT gets round it? BOXT's price shows the installation as being free, so were I lucky, I could get my gas run upgraded, something would go on the boiler, and I'd be able to return the boiler and get a refund on the whole job if you were right, but BOXT would have to leave my new gas pipework. I suspect it's one of those cases that would depend on who had the best solicitor, rather than being clear-cut.
As for my sarcastic BR example, yeah you got me, as it is a public service and it may be public record, but if so, you've missed my point entirely. Seriously, if you really don't get the sarcasm, I am more than willing to explain the joke.
which is their legal obligation under consumer law...
No. it is isn't, not if you are referring to the CRA, as your previous posts suggest you know. The manufacturer does not have the responsibility to replace a gas installer's boiler under consumer law as the installer is quite clearly not a consumer.
@hometech - you are quite clearly knowledgeable, but please be aware you are letting your psychological need to win this argument run away with you and you are oversimplifying the matter. This is coming across as point scoring to the detriment of the accuracy and therefore the helpfulness of your contribution to this thread. But thank you for your contribution, all the same.
Minster is referring to as a quotation and presumably has told the customer it is such: based on which the customer has instructed the work. Were this to become a court case, a consumer instructing work after a quoted price and then feeling the price is excessive would not have the judge's sympathy unless he can clearly show the price is well above that normally paid. Comparing online prices is not really comparing apples with apples and I'm sure the law would consider the overall price. The price for the parts supplied by the installer includes the installer's time to choose suitable parts, collect, and deliver them - much as the BOXT boiler prices include installation.
As you say, in doubt, consult a solicitor. But this is a plumbers' forum and realistically the OP needs advice on how to handle customers and avoid this situation. Writing a contract that will stand up in court but having to go to court over every boiler install is not a solution. Planning an entire business around one hypothetical awkward customer is not good practice unless the awkward customer is a £50,000 contract. Pimlico (a very successful business) has its Ts and Cs limited to 16 points and I suspect that any event outside of those terms is handled by informal discussion or it goes to court, otherwise it'd be like being in Italy where you get handed 25 pages to sign without a chance to read them and, while the contract is watertight (but possibly itself subject to litigation due to unclear terms), the plumbing itself may not be.
I would, however, be interested to see every line of written communication between the OP and the customer (with sensitive details omitted) if this is happening often. I'm not sure if it's how the information is presented, or it's simply a case of similar people referring Minster to one another.