Can someone take legal action against me if I cancel a reservation, we have no contract. Just been speaking on phone, email and text.?

Speaking on phone, email, and text can create a contract.  You say you have a reservation.  That can be a contract.  Generally, the hotel, restaurant, or other venue taking the reservation agrees to reserve a spot for the person giving the reservation on a specific date and time, and the person giving the reservation agrees to pay for the reservation if they don't cancel it by a particular time.  From what you write, it appears that the other side will claim there was a contract and you breached it. Without all the facts, I can't opine as to whether their claim has merit.