Thanks to everyone who has taken the time to provide a response - really useful insight given my inexperience with this.
I've cancelled our case with the online provider and am calling some of the local firms recommended above this morning.
Partner and I had an offer accepted on leasehold flat in Burgess Hill last week - now need to find a solicitor to get property off the market.
Been trying to find a conveyancing firm, which has been a bit of a nightmare thus far.
We've had a local firm send us the wrong docs initially and then...