I think what I would do in your position is to tell them in the lesson today that from now on you will be warmly welcoming in only those students with a pen. That you have nothing to lend or give. Ask them to make a note in their planners. All of them. "remember pen". That will cut a few down for next time. Then next lesson, cheerfully line them up outside the door and ask them to get out their pen, and those with them say "great organisation, come on in and have a go at the starter!" Those who don't, don't look cross, just tell them you really sympathise but you have no equipment to give or lend, you've run out. Ask them to come back when they're equipped and ready to learn. Close the door with a sad smile. Make it their problem. If they ask where to go, look confused and say "wherever you left your pen, I know you remembered it because you wrote a note. Be really quick please". Close the door. It infuriates them initially, because they want you to dance the No Pen waltz and you aren't co-operating. You're not being mean, you're just not allowing it to be your problem.
That has hands down got to be the funniest thing I ever read on Mumsnet.
Firstly, this is not an issue of organisation. They are not forgetful. They don't forget their phones, do they?
These kids don't WANT to be in the lesson. They don't WANT to work. That's why they don't bring a pen. So they can say "I can't work Miss, I ain't got no pen!" And that's why they break the pen - so they can say "I can't work Miss, that pen you gave me is broken." They don't think - well I am going to have to do the work one way or another so I might as well bring a pen, and after all I do want a good job one day! All they think of is: I don't want to do this work, what's the easiest way of not being able to do it. That's as far ahead as they think - to the end of this unwelcome lesson.
So if you say "No pen, don't come in to the lesson," they will be overjoyed. They will wander round the school and not come back. They may leave the school entirely. They may run around the building pulling faces at their friends through the doors. They will eventually come to the attention of SMT, which you'd think would be a good thing, but they will claim the teacher would not let them in the lesson so what can they do? "She wouldn't let us come in!" or "I'm looking for my pen!" Not THEIR fault. Yours.
A teacher who let 10 students out of their class to wander round the school looking for a pen would be under disciplinary/competency measures by the end of that school day.
If you're really lucky, some will have gone home and told their parents "Miss X said I'm not allowed to come back to school until I've got all new equipment" and you will have the parents either ranting and raving up the school or keeping their kids at home because "he had his stuff stolen and I can't afford to buy new, the school should be looking for it, and now you're saying he can't some to school . . ."
Honestly, seriously, that's how it would play out.
The idea might just work with nervous year 7s though, so it could be a way to go with the new ones. Although then they would wander round the school crying and you'd have Welfare on your back too.