Dniece has this for her school skirts - a logo near the waist that has to be visible, to stop girls rolling their skirts up to be too short
They used to have the logo near the bottom but girls were still able to display the logo after they'd rolled up the skirt, hence the change to its position...
I would email in (and get as many others to do so too - is there a school facebook page or twitter account that you can put the information on to make it as easy as possible for people) and point out that you don't have the budget to accomodate a 500% rise in the cost of school trousers (the £5 to £25), particularly without consultation. In order to comply could they please let you know how you can get hold of logo patches that you can sew onto the trousers yourselves in order to ensure that you dc can continue to wear proper logoed uniform... Because obviously you want to support the school but assume that as the government requires them to ensure that the prices of school uniform are reasonable** - and as the cost of the official supplier is now so high and unreasonable, you're sure that they must have a reasonable priced uniform solution - this is the only one that you can think of but obviously if they have a different one then you would be happy to use it!
**Can't remember what the exact wording of the government diktats about school uniform being reasonably priced are but I'm sure I've read it on here several times so somebody hopefully will be able to say. But it would be worth throwing this in their face at them in your letter in order to get your views in first and get it in writing first that it is unreasonably priced! And by suggesting that you want your dc to wear official uniform and are offering to sew on a logo (sorry, I know that's a pain for you!) it means that you are showing them a reasonable way to provide a logoed uniform (if say the patches were a pound or two each - still more money I know, but a lot cheaper than having it stitched on ready) and they are the ones that aren't offering any solutions or options - they can't accuse you of trying to sabotage their efforts in getting everybody to wear logos and smarten up, you are the one asking for a reasonable priced solution (as required by law) and they are the ones that are being awkward.
I would also ask them directly how much of a cut of their uniform sales they are getting from the supplier and ask if they are willing to forfeit this in lieu of having such an expensive change to the uniform. Or at least if they will make it an optional donation. Probably won't be a lot but it will concentrate their mind if there is no monetary benefit to them in the change.
Failing that I would be kicking up a fuss with the school governors and the local MP.
(I've just googled uniform requirements in schools and spotted this guidance document which might be of help in pointing out where their new policy doesn't fit with the guidance in being affordable and about the lack of consultation with parents and within the wider community and that it will act as a barrier to people wanting to join the school...)