I've got loads of accounts with GMX. For some I used my real details when I opened the accounts; for others I just made something up:
https://www.gmx.co.uk/
So you could get an email address such as ourgroup@gmx.co.uk without using your own details.
If you require your own domain name though (so that you can have addresses such as secretary@ourgroup.co.uk and treasurer@outgroup.co.uk) you'll need to pay for both the domain name (ourgroup.co.uk) and for the email hosting service which you'll be using, so you'll need to provide your personal details for the payments.