I used to do 26miles both ways with no shower at work up to twice a week. Full mudguards!!!
I had a bag under my desk with small towel, tupperware bowl, flannel, soap and deoderant and work shoes. I would get in get that, go to the disabled loos, give myself a flannel wash (for the older amongst us that used to be in the place of a bath 2-3x a week!) and use a pair of suit trousers, shirt, pants and socks from a small backpack.
Then I would eat the value of 52miles worth of diesel in decent food :D