There are two segwit address types (with 2 subtypes each): native segwit format, draft BIP173-encoded starting with bc1, and one embedded in the P2SH address (starting with 3).
You can create both in Electrum but the P2SH-embedded require either specifying BIP39 seed (with BIP49 m/49'/0'/0' path) or a hardware wallet. You cannot create such a wallet with the native Electrum seed only classic or pure segwit.
See, also my description of all nuances here:
https://bitcointalk.org/index.php?topic=2353665.msg24018980#msg24018980Native segwit addresses are probably not a good idea for a general user yet (but maybe excellent for, e.g. exchange hot wallet) but P2SH embedded are fine as long as you can generate them.
Thank you very much for the information, you saved me a lot of time searching for this stuff. I have read through some of the other thread you linked to as well but I just want to make sure I have understood correctly.
I've created a new Segwit wallet which has the addresses starting bc1. Am I correct in thinking that any Electrum wallet that is version 3 can send a transaction to these addresses but no other wallet can?
Secondly, (this is the bit I'm more unsure about) I can send from that wallet to all other addresses as the transaction is processed on the blockchain not by the receiving wallet?