Had this exact problem when I first set up my motorhome. Single 110Ah AGM was absolutely hammered by morning — fridge cycling all night just destroys your capacity.
Few things that made a real difference for me:
- Pre-cooling the fridge before you disconnect from hookup. Don't ask it to pull warm air down overnight.
- Ambient temp matters massively. Parked in full sun all day the compressor works twice as hard.
- Insulation around the fridge if it's in a poorly ventilated cabinet — some vans are shocking for this.
Eventually I just accepted one battery wasn't enough and went to a 200Ah Fogstar Drift LiFePO4. Night and day difference. Lithium handles the compressor spikes better and you can actually use most of the capacity without worrying about damaging it like you would with AGM.
If you're not ready to upgrade batteries yet, a small solar panel even 100w through a Victron SmartSolar controller will top you up enough to extend things considerably — especially spring through autumn in the UK.
What fridge are you running? Some of the cheaper compressor units are genuinely inefficient compared to something like an Indel B or Dometic. That could be part of your problem before you even look at the battery side.