At the Society's annual general meeting today 58 out of 88 solicitors voted to remove the current exception to its conflict of interest rules, which permits a single solicitor to carry out work for a client wishing to buy a property and their mortgage lender.
The Society will now bring forward new practice rules for its members to vote on at a special general meeting in September.
If voted through at the SGM and subject to approval by the Lord President solicitors will no longer be able to act for both buyer and lender.
Austin Lafferty, president of the Law Society, said: "This was a highly important debate to have and I thank everyone for their contributions.
“We can view today's vote as just the start of a move towards reforming and improving conveyancing practice and we intend to hold further discussions with the Council of Mortgage Lenders and others.”
However the CML seem less than impressed by the Society’s vote.
Paul Smee, Director General of the CML, said: "It is disappointing that a measure which is so blatantly against consumer interests and will impose added costs and added scope for confusion and delay has been voted through, with not even the pretence of wider consultation.
"At a time when housing and mortgage markets are still recovering, this is a protectionist measure with little regard for the interests of consumers."
But the Society disagreed as Lafferty said: "It's in everyone's interests, particularly the prospective house buyer, to provide efficient and cost effective services.
“Technology has improved things enormously and it's worth remembering that conveyancing fees in Scotland are moderate compared to elsewhere - it can be up to three times as much in Ireland.
“Market forces will also play a role and undoubtedly determine a new fee structure so, while the borrower and lender will each pay for the work of their own solicitor, I do not foresee any astronomical price rises."
Eddie Goldsmith, senior partner at Goldsmith Williams, added: "The practice of joint representation where one solicitor looks after the interests of both the lender and the borrower is well established having been the norm for the last thirty years and everyone is well used to this.
"Indeed the Law Society in England and Wales recently debated this issue and they felt there was no good reason to change as both delay and extra expense could come with separate representation.
"The conclusion therefore was that there was no benefit to the client from such a change.
"What this vote has done is to re-open the debate again in England and Wales as there is no difference between acting for a lender and borrower in Scotland or in England or Wales.
"This could have far reaching consequences for the house buying public and adds further uncertainty into a housing market which remains fragile."