It started positively for Bees, who had not earned an away point all season. Reading loanee Sophie Quirk burst forward after three minutes, with her shot forcing Eartha Cumings into a low save.
The first half was an attritional affair with few clear-cut chances but in the 42nd minute, the hosts took the lead.
Ella Rutherford’s corner ricocheted in the box, before falling to Heuchan who poked home from six yards.
Jess King should have doubled their lead in first-half stoppage time, but shot wide when clear through on goal.
In the 58th minute, Rutherford’s shot from the edge of the box was excellently pushed wide by Bees keeper Faye Hazleton.
Five minutes later, the hosts went 2-0 up as a clever free-kick was kept in play by Rutherford and sent into the Bees box. The visitors were unable to clear the danger and Sulola capitalised from inside the six-yard box.
Bees captain Georgia Robert was adjudged to have brought down Welsh striker Ella Powell in the penalty area on 75 minutes – and Clifford stepped up to confidently put the result beyond doubt.
Bees got a late but scant consolation in stoppage time as a scrappy penalty box skirmish came off a Charlton player – but the damage had already been done.
London Bees captain Merrick Will: “It’s hard to describe. We’re obviously gutted. We knew it was going to be down to the wire, scrapping with the teams around us. I think it was tight. But I think we’ve held our heads high, and we can pride ourselves on trying to affect our games rather than relying on other teams to drop points.
“It’s really gutting, especially with the group of players that we’ve got. We’re a really close-knit bunch. I’m emotional myself, so I’m sure the girls are feeling the same way.
“There’s still people at this club who have worked hard tirelessly. We’ve had the departure of Lee [ Burch], and Sian [Osmond] has done immensely well since she stepped up. All our coaching staff are here giving 100 per cent as well as the girls. We’re still representing the club and ourselves. We’ve still got a job to do. That’s what we’ll focus on.