I can't speak on the hotel choices, and you may get a better response in the UK&I forum.

The lowest through fares simply don't allow stopovers. At EUR34 each way before fees, I'm not surprised ! With stops, ba.com is likely quoting a much higher through fare that does allow.

I couldn't say why it is not quoting the cheaper combination of HAM-LON-HAM + LON-JER-LON. It's possible the fare rules prohibit combination on the same ticket.

Either way, there's no downside to booking separate tickets, as you're not making connections.

hth