If you are chain free, there is only one property being bought and sold. With chain free transactions, all parties will find that there should be a standard timeline to be followed until you can move in.
While this is generally true, there are other factors that can slow down the sale, even if you're chain-free, such as if:
the property is leasehold;
there is a mortgage;
the council is slow at returning the local authority search; or
the seller doesn't provide satisfactory replies to enquiries.