It would depend entirely on what Timatic says whether BA would allow you to board at ARN for London and a Schengen Residence Permit on its own isn't helpful information in this direction. If you are on Article 10 and your partner/relative is travelling with you then that's another matter. Once you get to London, your onward flight is from Terminal 2 so going via landside is not going to add much (you'll want to use the tube, not HEX) but you are at risk of being denied entry depending on a whole range of factors. You would then need BA to ship the items to T2 for you, which has been known but isn't quick. I would certainly ask ARN to through-check, but they aren't supposed to do this. To some extent I would have to query the wisdom of this. Since BA's baggage policy is known to you, and you appear to not have good entry credentials for the UK, trying to save time and money as well as not travelling HBO on separate tickets on separate airlines in different alliances with a Heathrow terminal switch, in, presumably, the middle of winter seems to me to be quite a risky approach. If the purpose of your question is "is it worth taking the risk?" I could only give you an answer in the negative, based on the limited information provided.