Conveyancing solicitors are frequently asked "How long will my sale take to complete?" or "When can we exchange?".
The problem is, much depends on what date you agreed with the seller/buyer before you instructed your conveyancing solicitor. Many conveyancers will ask their own clients what timescale they are working to, as most will want to help achieve them. Unfortunately, in the excitement of agreeing an offer, talking about dates will often have been overlooked by the agent, seller and buyer.
As a result, conveyancing solicitors can be forgiven for losing focus on how prompt they must be in the process, if their own clients are not even agreed over timescales. For them to then ask their conveyancer "when can I move?" is directing it to the wrong person. Only your seller/buyer can answer that, whether you speak to them directly, or you use the estate agent, but dates are a term of the sale, and that should have been negotiated at the start.
Clearly, if there is a chain of properties involved, agreeing an actual date is almost impossible as there are too many interested parties with their own agenda, and the chain may not be complete when one offer is agreed, so dates will be unknown.
However, talking with your immediate buyer/seller at the very beginning must be a priority, as at least you know what their plans are, even if they are approximate and dependent on their own sale/purchase.
There are many estate agents who are very good at agreeing dates at the start, many expressly write it on their 'Memorandum of Sale' which is circulated to the patties and their conveyancers. However, there are many who overlook it and even fail to get involved in much else after offers are made/agreed; certainly making no effort to chase the chain of conveyancers. Probably the most unhelpful type of estate agent.