Not really.
There's 2 snags.
1. It is no longer possible to create new btinternet email addresses
2. You might still encounter the problem anyway
It would be simpler to create another Gmail address and see if he gets the same problem with that
It is unlikely that all the BT email recipients will have blocked your father's email address but this might be worth a try.
Can your father contact at least one of the BT email recipients that is not getting the gmail to add the gmail address to their "Safe Senders" list by logging onto their BTMail account using a browser, not an email client/app, and then click on their username at the right hand side.
Select "Settings" then go to the left hand side and select "Mail". Scroll down and click on "Safe Senders" and add your father's gmail address to that.
While there they could also check their "Blocked Senders" list to ensure that the gmail address has not been blocked and also that the gmail domain has not been blocked. If they have been they need to unblock them by scrolling down the list until they find them and select it then click on "delete".
After they have done the above your father should try sending a small email to that individual.
If it now gets through he should send an email via a different email address to all the affected BT email addresses and ask them to do the same.