SFO - LHR - LIN in WTP two separate tickets was 4x cheaper than booking a single ticket I can't find a definitive answer on this, or I'm searching the wrong keywords. Sorry for perhaps an obvious question.

I understand BA won't check baggage through to LIN from SFO. Can I connect through T5 (both BA) without checked luggage and stay airside, or do I need go landside (3 hr connection which is ok but I'd prefer not to...).
If so, do I check in as usual online and use the boarding pass from the BA app?

Thnx