Specific questions get specific answers, but if I continue in the abstract, there are 4 factors here
- delay, in summary defined as being between 2 and 4 hours, but usually 3 hours. You suck that up, you may get compensation
- cancellation, range of rebooking options. But you do need a cancellation. A delay greater than 5 hours is a cancellation
- conditions of carriage, linked to the above since 5 hour delays are deemed significant and can trigger a refund. There is some wriggle room here since "significant" is open to interpretation.
- BA's rebooking policies from delays and cancellations. There is a lot to this, it stretches into 50 or so pages, so I can't easily summarise.
Now again in the abstract, if BA retimes the only flight of the day, broadly speaking your options are to move to the day before or after, plus currently FTV/eVoucher option. BA can argue that this is what you agreed to. In certain circumstances you can get a rebooking option from -2 or -3 days to +14 days.