Nope
Simple answer is no. The Law Society have the whole scene sewn up. The law says that only those who have purchased an insurance bond with The Law Society may engage in conveyance. And, funnily enough, the only ones who can get the insurance are solicitors !!!
If ever there was a contract in restraint of trade, there's one there.
The Competition Authority singled out conveyancing a number of years ago as being a market that's been quietly sewn up, but nothing was ever done about it. Too many politicians are lawyers, or in another protected profession for them to want to rock the boat.
And, as always, 'tis the poor auld consumer who picks up the tab