Yes you can. House-sharing is common in places like London where rents are sky-high and unless you are earning a high wage you simply cannot afford to rent a place on your own.
I once shared a house with a single man and a single woman. He then moved out so it was just me sharing with the single woman.
It would be very clear to anybody observing us that we were not involved. We simply shared a living room and a kitchen. That was almost 3 decades ago, before I was married. Things like that are even more common nowadays as rents are even more unaffordable for single people.