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It does look a bit full upfront, it's an A321 midhaul, so there are only CW and WT cabins, so in a way a potential double downgrade if it happens.
Yes you can ask to be rebooked, the compensation issue is a bit thorny at that point, but I would claim for delayed arrival if you went the next day, plus the hotel cost if it wasn't provided. The complexities are best explored in the dedicated thread for this, but I should point out that this suggestion isn't totally water-tight since actually BA do have the ability to downgrade and reimburse, it's allowed for by both conditions of carriage and the Regulation.
I would arrive no later than 3 hours before departure. The problem may clear overnight, it just takes one family to have a kid with chickenpox and suddenly there's no problem. More plausibly, a failed connection tomorrow (or an ex CAI TP runner missing the last leg!). So it's quite possible everything will be fine tomorrow, assuming the OP is ticketed. If not, give the connections you are happy to take instead (Alitalia? Austrian?) and/or you are OK to travel the next day. However I see that flight is also looking rather full too...... Meanwhile MS is sending half empty 777s over to London, it would appear.