So you, as a man, are going to a store, buying women's clothes for yourself, and you are embarrassed if questions are asked who these clothes are for.
Well, if I, as a man, go to a store, buying women's clothes for my wife, nobody asks me questions. Why? Because the store employees figure out the difference, and while most are decent people and don't try to embarrass you, some are different.
To fix this: You need to change your attitude. Before you go to the store, stand in front of the mirror and tell yourself that you are buying clothes as a present for your wife, or for your girlfriend. Repeat it until you believe it. Then you can go to the store without problems. Allesandro's advice saying "I am buying this as a gift. If the size doesn't fit, can I come back and change it?", that is pure genius. Because no man can be sure that clothes will fit his wife. And you state the "buying for my wife" out there as a statement.
If you buy underwear, well, I would find it a bit embarrassing myself to buy underwear for my wife, so that is normal. Two ways to handle this: For everyday items, look them up on the internet, take a note which item from which popular brand that the shop will have, and which size, and then you go to the store, look embarrased, and show some salesperson the note, saying "this is what my wife wants". Or you are buying are buying a birthday present, or a present for an anniversary. So you go to the store and ask them for advice. You should have the size ready, and you would want something that is nice as a present, but not too adventurous so you don't get into trouble with your wife.
Now let's say you do run into a problem with someone who pesters you and doesn't let go. So what would I do, as a husband buying clothes for his wife, and some idiot salesperson seems to be getting the wrong end of the stick? I would be annoyed. I would be very annoyed. And I would let them know that I'm annoyed. I would ask "What is your problem? Would you like to get a manager here and we discuss your problem with them and then you can explain to your manager why you are losing £150 worth of sales?". Remember, you are buying clothes for your wife. You would be just as annoyed as I would be. And you would answer in exactly the same way. Not embarrassed, but angry.
PS. You can avoid the whole thing by buying online. And if you have nosy neighbours, you can usually get things delivered to some store, or some pickup location. And it's absolutely normal that a woman would order clothes, has them delivered to a store, and then the husband picks them up.
PS. To down voters: 1. The OP didn't mention his age. 2. The OP explicitly mentioned that he was willing to lie to avoid problems. 3. There would be no "false outrage". We are talking about an employee sticking his nose in my private business. The OP would be just as outraged as me. I explained a strategy that works, and why it works.