I havent read the how to complain
it probably starts with a complaint to the firm
and then
( that is exhaust local remedies)
and here is a solicitor I complained about before
https://www.casemine.com/judgement/uk/5a8ff73260d03e7f57ea9738
bear in mind that you have not had a loss - and so there isnt much to complain about -
you would have had questions as to title if you had tried to sell in the mean time but didnt (this is called suing on a chance, and just about gets up and runs in contract law)
so I would go for a reduction in your fee ....
This happened to me - bought 1999 and title perfected 2004 where I had bought from the receiver of a bankrupt estate of a convicted criminal - and the Asset Recovery Service asked me to prove it wasnt still his ! oo-er Mrs ! I did, plenty quig