Google the pet fostering team.. or look at this page (altho there are many more) Volunteer Pet Foster Schemes, including Dog Foster projects, Cat Fostering ..... im sure they will help if not point you in the right direction...
my friend was in the same situation as you a while ago and filled out the forms the scheme she used was confidential however the organisation only use reliable people and give you regular feedback about your pet. they make sure the pet is reunited as soon as the owner is able to have it back.
hope this helps!
i wish id known about it a few year back when i was in that same situation.. unfortunately after 3 months my dad who was looking after my dog gave up and i had to give her to a shelter

good luck