OP, this is the process:
Once offer is accepted and generally survey done, the solicitor draws up the contract and will ask you to sign it, ready to exchange.
Exchange is when the solicitor gives your contract to your vendor, and puts your deposit in your vendors solicitors account. At the same time your vendor gives your solicitor their contract which says they will sell you the house.
If the vendors are buying another place, they likewise exchange contacts with their vendor and pay the deposit.
All these contracts have to be exchanged on the same day, simultaneously, because otherwise someone could be under contract to buy a house… but not have the money from their sale. Or else be left without a house. Hence a chain.
All the contracts in a chain will specify the completion date, the date when the balance of the money is paid and everyone in the chain becomes owner of their new house. Again, this will be the same day.
So while everything to do with the purchase of your house may be ready, other people in the chain may not be.
The EA should be giving you a regular update. Your solicitor should be able to tell you whether your own purchase is ready. Are the searches back, all enquiries answered etc. Ask your solicitor when you need to be ready to transfer the deposit.