But the company - the biggest mail-order wine business in the world - insists it remains keen on opening more traditional shops.
It already has nine stores and is actively seeking more in the Home Counties, though it admits progress has been slow due to a shortage of suitable sites.
Head buyer Peter Greet described Fenchurch Street as "an idea that was ahead of its time".
He added: "The signage was difficult and people didn't know what they were coming into. People have been programmed to go into an off-licence and take away a bottle of wine and it was hard to get over to people that they couldn't do that."
Greet said Laithwaites had not put a figure on the total number of shops it was aiming for but said the traditional retail business was "more than a sideline".
He added: "They are another channel to market that we're still learning about - the picture on the high street is very fluid.
"We remain interested in opening new shops if they're in the right locations. People still want to see and feel the bottles and there is a pleasure in buying wine from people who sell well."