Leafe face a crunch clash tomorrow against a side whose form suggests they have begun to find their feet in the division.
But English's men are just two points above the drop zone after three straight losses.
The latest was a humbling 4-0 reverse at Hythe Town on Tuesday, after another defeat in Kent last Saturday, 2-1 at Whitstable Town.
English says his players must sort out their attitudes if the club is to avoid playing in the Combined Counties League next year.
"Quite simply two or three players are not working hard enough for the team and that has got to change," he said. "I am pretty glum at the moment but we will sort it out, even if it means telling some of our more talented players that they have to find a new club.
"Grafters keep you in this division, but at the moment while we have a set of talented players they are not doing enough when we don't have the ball.
"If they don't want to pull their weight they should drop into the Combined Counties League where they can afford to coast and get by on their talent, but they can't carry on doing that here."
English admits he is losing patience with his young squad, which he says has more talent than at this stage last season but is failing to turn that potential into points, having won just three of their nineteen games this season.
"We should have got at least four points from our last two games but we have come away with nothing," he added. "Our midfield and forwards are not doing enough when we give the ball away. You can't rely on your back four to do all of the defending at this level as they are regularly being out-numbered.
"We have to look at our individual decision-making, too. On Tuesday we had players taking four, five and six touches trying to run round three or four players and score. You could watch 20 games this week and not see a goal like that but some of my players think they can do it.
"Too many of them are playing for themselves, not the team."
English says he will not walk away from his position at Church Road despite becoming increasingly frustrated with seeing his side underachieve. But he will wield the axe if performances do not improve.
"We have to put where we are into context of what our objectives were at the start of the season," he said. "Our objective was survival and to do that we need to get to forty-two points – a point a game.
"We have fourteen points from nineteen games, so are five behind schedule. That can be made up but we need to change things round now for that to happen.
"Our budget isn't enough for me to bring in the players I believe could turn us into a top four side, but too many people seem to think they are doing the club a favour by playing just for expenses.
"Financially, my hands are tied. But I knew what the situation was when I took the job."
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