Here's an approximate Timeline, which would be average for most transactions:
Week 1 - Offer accepted from buyer. Seller and Buyer instruct their solicitors. EA sends out the Sales Memorandum to each party - i.e. each solicitor, seller and buyer.
Week 1 - Buyer's solicitor sends welcome pack and initial instruction documents to buyer to complete, sign and return. The buyer will need to provide ID. The solicitor will do ID and AML checks. No work will begin until these early stages are complete. The solicitor will probably want some money paid on account in order for the solicitor to start work.
Week 1 - Seller's solicitor sends welcome pack and initial instruction documents (including PIF, F&C, LIF etc) to seller to complete, sign and return. Seller to provide ID. The solicitor will do ID and AML checks. No work will begin until these early stages are complete. The solicitor may need monies on account to pay for Land Registry documents.
Week 2 - Once Sales Memorandum received, buyers solicitor and sellers solicitor send each other an 'initial' letter introducing themselves to state that they are acting in the transaction.
Week 2 & 3 - Buyer and seller return completed documents, monies etc. to their respective solicitors.
Week 3 - Seller's solicitor gathers/obtains the initial documents required to form a draft contract pack, i.e. Land Registry title, plan and transfers noted in the title, together with the F&C, PIF and any other necessary papers such as certificates and warranties provided by the seller relating to the property. Seller's solicitor will draft the contract.
Week 3 - Seller's solicitor will write to seller's lender to obtain an up to date mortgage statement. They will write to any freeholder/management company to obtain details of any management pack needed and the associated fee for providing it.
Week 3 & 4 - Seller's solicitor will send the draft contract pack to the buyer's solicitor and will ask them to confirm their approval of the contract, provide a draft transfer and raise any initial enquiries.
Week 4 - Buyer's solicitor receives the draft contract pack together with draft contract. The buyer's solicitor will now need some time to peruse all the title documents and the F&C, PIF etc before they can be in a position to raise enquiries. Bear in mind, some legal documents are lengthy and it is therefore a fairly lengthy amount of time to properly go through everything. Solicitors are busy with other clients too, so perusing these documents is not done in a day, more like a week or more.
Week 4 & 5 - Buyer's solicitor will check the buyer's mortgage offer and will often wait until this is received before ordering searches, providing they have received monies from the buyer to pay for these. Searches can take several weeks to receive - the local search usually takes the longest.
Week 5 - hopefully all searches are back, mortgage offer is approved and the seller's solicitor, having perused the draft contract pack, is now in a position to start initial enquiries. Don't think that the buyer's solicitor will raise enquiries before searches are back, they often don't because they like to do things in one go, rather than piecemeal.
Week 6 - The seller's solicitor will go through the initial enquiries, answering the questions that they can answer and referring all the others to the various third parties, i.e. the seller, the lender, the council, the land registry, the management company/freeholder etc. They may wait until all parties have responded to the enquiries before forwarding them together to the buyer's solicitor, rather than send them piecemeal. Bear in mind, that answers to enquiries may result in further additional enquiries being raised by the buyer's solicitor.
While this is an "average" timescale, it does give you some idea how weeks can go by with a seller and buyer both thinking that nothing has been done. There isn't a lot of progress achieved so far in the timeline above, as the preliminary (or pre-contract) work has only just been completed. The actual legal work doesn't really start until this point, i.e. raising enquiries and progressing the transaction to exchange and completion.
I'm not a solicitor, but have extensive experience working for a conveyancing 'factory'.