As a solicitor I can promise you that we are one of the most (if not the most) regulated profession in the UK. The SRA (our regulator) happily strike off solicitors at regularly intervals. Estate agents are the "profession" with very little regulations...
If you can prove a solicitor is lying then they will subject to an investigation and potentially struck off. Please see this.
https://www.sra.org.uk/solicitors/handbook/code/content.page
The problem with conveyancing (I don't practice in this area, but I am going through a purchase/sale of my own) is that solicitors charge very little for the service and indemnity they provide. If it goes wrong, solicitors not agents pay the price through their insurance. This means that more often than note the quality of service has taken a bit of a dive as the costs/profits have been taken out. This would be the same in any business.