On the outbound, DL may be willing to check your bags through DSM-MSP-LHR, even on separate tickets. They definitely won't check through onto the onward LHR-CPH segment. So you would have to go through immigration at LHR, collect bags, and then recheck them.

On the return, BA definitely will NOT check through on separate tickets so you will have to collect bags at LHR and recheck with DL. And while DL may tag through to DSM, no matter what you will have to go through immigration, collect bags, and go back through security at MSP.

As this will all be separate tickets, especially the LHR-CPH/CPH-LHR tickets, make sure to give yourself several hours in case of delays because if you miss any of these flights, none of the airlines are obligated to recommodate you on a later flight without you buying a completely new ticket at walk up fares. Remember to give yourself time to disembark the plane, go through immigration in most cases, collect luggage, stand in line to check luggage back in (with most airlines requiring baggage to be checked in 45-60 min before a flight), and go back through security.