Lynx most Solicitors who do conveyancing are quite trustworthy, but rather slow - and usually need for you to actually 'them' to keep your file at the top of their pile.
My only experience of an on-line conveyancing company was very bad. When I was selling my house last yeare, small chain just three of us. The people at the bottom used one of these companies. When it came to the time we were exchanging contracts, it was held up for days, as this on-line conveyancing company was not able to be reached by anyone. Emails, phones call, etc from solicitors, Estate Agents, the couple themselves were all totally unanswered. Their so-called 'office' was not a real one.
It was getting desperate, as I needed to complete within a few days to be able to move on my chosen date. My lovely EA spent nearly a whole working day just trying to contact this company. As did Purple Bricks through whom the couple using them had purchased. Took four very fraught days to get a reply from them.