Advise on conflict of interest with solicitors

Hi everyone,
I have recently purchased a property (first time buyer), my solicitor who was recommended by the estate agents was AWFUL to which I have taken to the ombudsman. My big question is, I have searched LinkedIn and found out the solicitor I used have the same managing director and several employees as the solicitor that was used by the person I purchased the property off.
Is this a conflict of interest??
I have had many issue with my own and the vendors solicitor about the same issue to which I have tried to complain to which is how I found out he has both companies.
I have been advised to go to the sra but not really sure what this comes under?
please anyone can you help.