a couple of misconceptions
Overall, a very sensible, rational article. I won't pass comment on the details of UK administration, but those are not important to the overall thrust of the piece.
On a carbon tax, two or three misconceptions seem to be floating around.
First, it doesn't matter where you place the tax, it can be anywhere at all in the supply chain and the effect on prices, consumer behaviour, and manufacturer behaviour is the same. Economics 101. Same with any cost or any tax. (Of course, there may be practical differences of implementation: naturally, you place the tax at the point in the chain where it is easiest and most efficient to administer.)
Second, it is vital to avoid the mistake Australia made. Australia exempted imported goods, which was madness. The carbon tax became a powerful incentive to close down your local plant and import stuff from China, which at that time was a relatively high-carbon economy. Result: pain at home and less carbon abatement than there might have been. (I should note that even so, the carbon tax significantly reduced emissions in a remarkably short time. Sectors exempt from it (imports, motor fuel, agriculture) continued to increase emissions, but many other sectors improved a great deal. Since the tax was abolished they have started to get significantly worse again.)
Third, it does not matter in the slightest what you do with the money raised by the tax except insofar as we all have an interest in taxation income being used to some worthy purpose. The main benefit of the carbon tax, just like that of tobacco taxes, isn't the income the government gets from it, it is the expenditure on the part of economic actors like consumers and manufacturers. Because high-carbon goods become more expensive, consumers find ways to avoid the tax by buying cheaper, low-carbon substitutes, and manufacturers find ways to cut their costs doing things in a more efficient way. As pointed out in the article, the government does not and should not specify how manufacturers and consumers avoid paying the tax (and thus produce less carbon), the market figures that out. Markets are really, really good at doing that. It's what markets do best.
Still on the third point, once we understand that spending the funds raised by the carbon tax is largely irrelevant to its purpose, we are at liberty to do anything we like with the money. It still works just as well to reduce carbon regardless of whether we spend it on schools and hospitals, fighter jets, income tax cuts, perks for politicians, education, research, paying down debt, building wind farms, foreign aid, buying a billion tons of boiled lollies, or even just shred it and bury it in a big hole. There are individual benefits and problems with each of these possibilities, of course, and we are free to debate the merits of each one, but the key point is that these don't matter so far as the benefit of the tax is concerned. If you want to spend the tax on solar PV collectors or whichever other renewable technology you prefer, that's fine, but it will still work almost as well even if you go the boiled lolly option.
Fourth, once we understand that the tax income is fungible, we can immediately see that there is no "right" level for it. There is a minimum appropriate level, which depends on how much high-carbon activity you are aiming to take out of the economy and replace with low-carbon substitutes, and on how fast you want that transition to happen, but provided only that the total tax take as a proportion of GDP remains where you want it (at the current level, for example) there is no particular maximum appropriate carbon tax. Set it as high as you like, provided you reduce or abolish other taxes to compensate, and also provided that you don't ramp it up so fast that it disrupts the whole system. Economies can cope very well with change, especially known, expected changes, but very large, sudden changes tend to cause trouble, so phase it in over a few years, increasing a little at a time until it's where you want it.
Personally, my preference would be to start removing other taxes one by one as the carbon tax increases, starting with daft ones like (Australian) payroll tax (a tax on jobs! How dumb is that?) and working through as many of the others as possible. What is your most-hated tax? VAT? GST? Income tax? Poll tax? No reason we can't get rid of it and have a carbon tax instead.