After the test Rapid Swiss tournament test on Thursday, I believe that we should be able to run rapid tournaments. I have still to investigate other formats.
I believe that you can become a chess.com member (bronze level?) for free. This allows you to enter ONE tournament at a time.
Thanks to the information from Austin, I have also created a Team "Glasgow Polytechnic" on lichess.org. This website is totally free. I know that it also allows you to set up tournaments. I will be investigating this system over the weekend.
I just thought today that you might not want people to know your real identity. If you are happy to send me your handle then I will keep them safe on a spreadsheet on my computer. Send me your handles and please state if it is for lichess.org or chess.com.
If you know of another suitable online chess website that we might hold tournaments, then please let me know.
Ken Stewart Quickplay (online) on Thursday 30th April should be able to go ahead in some sort of online format - I hope!
Keep your social distance.