First up, RP has moved production back to the UK and the quality does seem to have gone up. I bought a 1 inch long handled scraper and it does seem to hold its edge rather better than earlier RP tools I have. Its subjective though. Its not 'fancy' but it feels right and well put together - sturdy handle and ferrule. UK made probably increases unit cost but shortens supply chains and means you don't need to order a year in advance or hold as much stock to match unpredictable demand.
Second - inflation and VAT. Inflation is compounded, the rpi index in 2006 was 202, now its 323 so your £99 gets to £158, add more VAT (its 20% now, was 17.5) you get to about £163. Assuming the £99 set was 6 piece not 5, and was bought full price rather than on promotion it still looks like a significant price hike, but certainly not in the 'joke' territory. RP often do time-limited discount promotions, so that would bring things much closer.
Third, and this is the big one, is that assumption that cost and retail price are linked. They are for some things but not for others. I buy heating oil (rural) and that is a commodity - suppliers can differentiate a bit on service and ease of ordering but 28 sec Kerosene is the same whether I buy it from Goff, Gulf, Watson .... whatever. A big part of the cost is their purchasing cost, a small part may depend on how efficiently they run their tanker fleet, so I buy on price. Frozen dead chickens are in the same category - Tesco, Asda, differ in what the bag says but they are a commodity. Producer costs rise - retail price rises.
Consumer goods are different because they are differentiated by quality and 'perceived quality'. A BMW will cost a bit more to make than a Skoda perhaps, better plastics and trim, but not a lot more. But people pay lots more for a BMW than an equivalent Skoda because they percieve it as "better". Price is driven by what the market will pay, not by what it costs to produce. (as long as A>B, otherwise you go broke). Does a Roberty Sorby gouge cost twice as much to make as a Crown? Doubt it. Does an iphone cost twice as much to make as a Xiomi? Your house, not exactly a "consumer good" but subject to the same quality perceptions (if you are fortunate to own one) is worth what someone will pay for it, not what it cost to build or cost you to buy.
It looks to me like RP has decided it might not survive as a bottom-feeder budget brand: they can always be undercut by someone on ebay or alibaba. So they are moving upmarket - not to the top but to the middle where there are decent margins to be found. You do that by increasing quality, increasing the perception of quality which has a lot to do with presentation and intangibles, and of course the price. Look at what others are doing, decide where you want to be and price accordingly. I try not to buy stuff that is "too cheap", and don't want to shell out on brands for brands sake. Look how Kia and Skoda have moved their brands from where they were 10 or 15 years ago - Kia were making and selling rebadged Mk3 Astras, now they have EVs that are sought after as best in their sector.
So yes, the price has gone up a fair but more than inflation but maybe with good reason. If they don't get the sales they expact they might well discount in a limited promotion: 25% off brings it pretty close to the £99 plus inflation. And we will all see it as 'better' - £225 with £50 off is seen as better quality than £175.
(Lie Nielson always were top of market - maybe they have good margins, realise that any more price hikes will damage sales, so have only made small adjustments).