Sometimes, maybe. Estate Agents will often recommend services of a particular conveyancing solicitor. In many instances this is because they have a historic partnership and because the Estate Agent is paid by the solicitor for referring your business. Be sure that you’re not paying over the odds for conveyancing fees so that the Agent can get paid.
The Estate Agent rarely has more influence over the conveyancer to get work done any quicker however, you might be happy with their recommendation and the fees quoted and decide to go ahead with them.