We sometimes have stray cats turn up on our doorstep, they've usually been dumped in our cul-de-sac. The last one we had was with us for 13 years. Recently another turned up and we took it in. It has been with us for some month's. Although we have a catflap and make sure that it can get out at anytime (no shut doors) it recently relieved itself on the dining room carpet. I cleaned it up and shampoo'd the carpet (forgive the pun, it was no sham).
Again the day before yesterday it happened, it wet on the mat inside the front door, I grabbed it and tried to put it out but it refused, then relieved itself on the lounge carpet. That was it, OUT, locked the catflap. It hung around looking so dejected, I fed it (outside) and eventually made a bed up for it in a crate in the workshop, which it seems to have accepted. There is a catflap in the workshop door. At least if it relieves itself in there I can clean the concrete floor easier.
LS, why not try a cat litter box, and fill it with cat litter granules, (this can be bought from any shop for a very low price) you can buy the boxes from ebay, then see if your cat use's it in the shed,
if so he or she can come back in your home before the winter ;) ;) but only allowthe cat in one room at a time, just in case ::)
this is what i - we did with ours, our's were both strays, the grey one is only a few months old now, black one 6yrs,
(http://img222.imageshack.us/img222/3919/image011nr8.th.jpg) (http://img222.imageshack.us/my.php?image=image011nr8.jpg)
(http://img175.imageshack.us/img175/9870/image006ms3.th.jpg) (http://img175.imageshack.us/my.php?image=image006ms3.jpg)
hope this helps
The cat was sitting around the yard, so pathetic, that I relented and bough a large square washing up bowl from Tesco's and a bag of litter and a scoop/sieve from Morrisons, Then the cat was allowed back in the kitchen only, where the cat flap is. Seems a lot happier now.