The usual issue is a mail sender suppression listing of your email address. Schools usually use a mail sending service. The school admins can see their sent mail outgoing to the mail sending service. What they may not see is notification that the mail sending service has had trouble delivering to your email address after retrys and therefore their senders have automatically added your email address to a suppression list and no more mail messages will be sent.
The fix is to ask the school reception admins to contact the service operating the school email and for them to request the email admins for the mail sending service to remove your address(es) from the suppression list or whitelist your email address(es) if that option is available.
The Scottish rugby email domain is sru.org.uk and this has a number of mail senders listed but the main one looks to be Mimecast. Mimecast does have a whitelisting option that's available to the email admins via a control panel access. The other mail senders are Mailgun and Amazon SES and both of these operate mail sender suppression lists.
You mention a Blocked Senders (Filter) list. If your TalkTalk Mail accounts have inherited a Blocked Senders Filter rule from the former mail platform that was in use prior to 2018 then just delete that rule. It's way out of date so probably ineffective and could be blocking any Mimecast, Mailgun or Amazon SES mail messages so best to remove it completely.
