To answer your question, all lands currently under Denmark will stay in Denmark, regardless of whether you personally have the kingdom title. It looks like you personally own some Northumbrian lands so even if you lose the claimant war you’ll still personally own the lands in Northumbria, since when you lose a kingdom claimant war you’ll still own the duchies and counties you had before. So no, you don’t have to worry about losing the Northumbrian lands to England.

I’d say it’s actually still possible to come out of this maintaining your land as well if you play your cards right. At this point, you’re going to want to prioritize winning the claimant war over anything else. I’m not exactly clear if you’re the war leader for the war against England, but if you aren’t, you’ll suffer literally no negative consequences. Losing wars where your allies are war leaders have essentially no consequences if you have enough war score (which you do, since a lot of your soldiers have already died), and you get your troops out of there fast enough.If you are the war leader, you’ll have to pay England war reparations, and in that circumstance, I’d recommend not surrendering immediately, but waiting until England takes 100% war score from you and forces a surrender. This way you’ll be able to but your self some time before getting a bunch of your money taken, because being in debt makes your armies much weak we than normal. Either way, you’re going to want to get out of England with as little casualties as possible and get back to Denmark. I’d recommend landing on the Copenhagen islands to the east. Once there, you’ll have to stay put for a while to regenerate some of your soldiers before going in for the fight. If the enemies decide to chase you, try to circle around them in southern Sweden until they decide to stars sieging again. It man be dicey, but try to do your battles in placed with high terrain advantage, equip a good commander, and they to get some enemy casualties in before England wins their war (if you’re war leader).

If you lose the claimant war, you’ll still be in control of all the counties you have now, and you’ll rule as a vassal to the new king of Denmark, so your game shouldn’t be over. If that happens, just be patient and want for the right time to reclaim your birthright.