It is indeed the auctioneer who will notify the sale details to your solicitor. But this should not be the first inkling the solicitor gets that there is a sale in the offing. I think there are previous posts about this, but at risk of repeating them:
1. It can take a couple of weeks to get up title documents from a lender.
2. When the solicitor receives the title documents, it might take another few days to get to drafting the contract.
3. In this market, you should have your solicitor under starters orders. So you should notify him\her when you are putting the house on the market.
This means that your solicitor will have got the deeds and done about 80% of the work in drafting the contract, so that when he\she hears from the auctioneer, he\she can get the contracts turned around pdq.