There's quite a few websites you could try:
Horse deals
the horse exchange
Ad horse
Horse and Rider UK
Equine Adverts
Preloved
Horsemart
Project Horses
NFED
But probably the best way to find people is through word of mouth, so I'd suggest putting ads up in local tack shops etc.
Good wording, good pics, patience for the unsuitable idiots who waste your time, an ability to trust your gut instincts and not get disheartened as the what seems like 90% of owners have horses for loan so it's a loaner's Market. Hang I'n there and good luck.
The best one i've found so far is Preloved. Be on your guard though - people have a high opinion of their abilities (IMHO) and you do get some joy-riders/beginners trying their luck. But generally speaking if your honest in your message you do get the right people replying - there's also wanted ads. I found my current part loaner through there - granted after a couple of non-starters.
Word of mouth is good if you're on a large yard or ads at local larger yards/riding schools - depends on what sort of rider you need for your mare.