The easiest solution would be if there is a shop local to your work that will wash and iron your shirts. That will usually be £1.00 - £1.50 per shirt, so you'll need to decide whether the convenience is worth the cost.
What I do is to fold my shirt in half just offset from the buttons, then fold the sleeves in. Place your socks and pants at the bottom to give it some extra bulk, then roll up from the bottom to the collar. Roll tightly, but be careful to keep the roll crease free. You will still get the odd crease, but should be presentable. I tend to take a weeks worth in my pannier on a Monday, so that if I want to take my quick bike (no pannier) I have that option.
My shoes and trousers stay in my desk drawer, and I rotate my trousers round every couple of weeks.
Also, sit at your desk for at least 10 minutes after you arrive to cool down, otherwise you'll sweat all over your clean shirt. Quick wet wipe under the armpits and nads plus a small spray of deodorant and you're good.
