Why would it not work? Have you tried it yet? Private keys are ALL derivated in the same way, so it wouldn't matter if it is created in a wallet X 10 years ago, or in wallet Y 10 minutes ago.
Do make sure you're using the right electron cash, and that you're not running a scam wallet, (check the signatures of your download etc.) Otherwise all of your bitcoin cash AND bitcoin might be lost.
Thanks AdolfinWolf. No, I have not tried it yet. I made some stupid mistakes in the past and almost lost my bitcoin. That is why I want to make sure I don't make a similar mistake again.
The keys were generated with Multibit long ago. When I recently entered the keys into Electrum it gave me the message: Warning, imported keys can not be recovered using the seed! That gave me the idea that the keys must be generated by, and somehow connected to, Multibit. And when I would enter the seed into Electron Cash, it would not see the imported keys. Does my reasoning make sense?
I could simply try it, if you think nothing bad will happen. I hope you understand why I am being very careful here, I got my bitcoin back and don' t want to jeopardise that again.

Is Electron Cash dedicated to Bitcoin Cash only? Can it in no way interfere with my bitcoin BTC?
If the seed was generated in MultiBit, then you need to import your BTC wallet using the seed in MultiBit. There you would get a list of all your addresses. You may then copy the Private keys of all the addresses with balances and use Electron Cash to import in a new wallet to claim your BCH.
If the developers of electron cash have malicious intent then they may get your btc from your private keys because it is NOT the official wallet by Electrum !
So I recommend you to transfer your btc to a new address, just to be on a safer side.