I'm surprised at all the people saying things like "how will they know where your clothes are from" or "buy <cheap brand> and have it altered".
Now, it's true that lots of high end brands (and lots of rubbish ones) are wildly overpriced. You can get top quality tailored clothes for a fraction of the price of most hoity toity brands - say £1500 for an off-Row bespoke suit compared to £5k+ on the Row (back when I bought such things anyway).
However, it's obvious from looking at something like a suit whether it's decent quality. Good fabric looks completely different from cheap, not to mention lots of high st stuff is synthetic blends that stand out like a sore thumb. Proper hand-canvassed, tailored construction is easily distinguishable from mass produced fused suit coats. Plastic buttons just do not look like proper mother of pearl shirt buttons or natural suit buttons.
So yes, if they're the sort who have a problem with you not presenting a high-end appearance to clients and colleagues, they're probably the sort who will easily be able to see whether you're wearing quality. So there's that.
And I think in many cases it's fair enough to make such a request. If you're running a high-end business you need to present a polished image to clients, competitors and to the rest of your team - it's not just about marketing, it's also about maintaining a culture of excellence, and it's important. I've worked for and run such businesses. At one point early on, a boss told me I had to replace my Ford Focus as it wasn't an appropriate car in which to be seen arriving at a client's office. And he was right, it wasn't.
BUT, and it's a huge, huge BUT:
If your boss wants to run a high-end business where staff are held to such standards and expectations, and generate a correspondingly high-end income, Then. They. Pay. For. It.
Either your salary reflects the cost of dressing for your job, or - like some firms I've worked with - they have a corporate account with a Savile row tailor and heavily subsidise your bespoke wardrobe.
If they won't pay you a high-end salary or directly pay for the wardrobe, they don't get to demand it.
I once worked with a lady who'd spent some years as a young associate at a top magic circle law firm. When she worked an all-nighter, she would go buy a new, good quality blouse and suit in the morning and expense it to the client. She soon had an extensive and quality (if off-the-peg) work wardrobe. Food for thought perhaps.