The outage lasted a LOT longer than 75 minutes.
I expect downtime, which is precisely why I have two separate Internet connections at home that run on separate infrastructure (BT's Infinity, Virgin Media's VIVID) and if I have to, I could connect my Vodafone 4G dongle, but my router isn't setup for that currently. Honestly, switched over within the first 5 minutes and had no problems the rest of the day.
tried repeatedly to get into BT webmail all morning
I'm shocked you use BT webmail though, it's never had a good track record and doesn't that lock you in as far as ISPs go?
The BT-supplied router, the fornicating clunky useless and slow Home Hub 5, does not allow you to put in your own DNS servers.
If you can get the BT openreach modem, you can put any router that supports PPPoE on it.