Yes I did read the original post, and the OP has some perfectly valid concerns. I would hope that the management would take those into consideration, in fact there has been no indication yet that they won't do so.
As it happens I have worn uniforms for work twice.
From the OP it seems clear to me that she and her colleagues are not in a strong negotiating position. They are already concerned about being made redundant, and the numbers of unemployed in this country are rising.
What do you mean when you say you're not sure why I have gone on this track? Sorry I don't understand your meaning there. I am giving my viewpoint just as you are. I am also confused as to why experience negotiating as part of a large company from the management point of view (as you have assumed I am) doesn't count as being experienced at employee negotiation..
Anyway. If I were involved in this negotiation it would go as follows
Me: Hello lovely employees. We are proposing to introduce a uniform. These are the good business reasons why we would like to do it:
a
b
c
And these are the reason why we think it would be good for you as well
x
y
z
We have no doubt that some of you have concerns and we would like to hear them and to hear any alternative suggestions or proposals you might have.
I would then expect anyone who objected to say so and to explain exactly why. I would then try and negotiate their cooperation by attempting to address those concerns and listening to their proposals. I gave the OP some ideas to use as alternative proposals in an earlier post. I would hope most reasonable employers hoping for cooperation would at least consider those and take into account those concerns.
If someone instead of saying what their concerns were and proposing alternatives said 'I just don't want to and I won't unless I get a pay rise', that would not put me in a mood to play nicely myself quite honestly. I would say 'Oh really Susan? Well if you feel you need financial compensation to wear a uniform, you must have some pretty serious concerns about doing so, lets talk about them and see if we can address them.' If it was for cost reasons, I would bear that in mind and definitely consider it, and would expect some figures about increased costs.
And so on.
But I would bear in mind the following
It's a perfectly valid and fairly minor change to make, and there are good business reasons.
The employees are not in a strong position as I said.
It's perfectly possible for an employer to force through a change as long as they go through the necessary steps to do so. It comes with a risk, that the employees will claim unfair dismissal if that happens, but as an employer I would consider the likelihood of the employees bothering to do that and of them succeeding if they did (not very likely), and if push came to shove and they absolutely refused that would be an option.
As you say, disgruntled staff will adversely affect productivity, which is why I would only see that as an absolute last resort and would instead listen to concerns and address them.