Boys
Axel - fine, pronounceable
Casper - fine also
Bent - definitely not
Mikkel - nice
Niels - nice
Søren - I think it would be pronounced very differently from the Danish way, there would definitely be two distinct syllables, but if you're happy with that I think it's ok. The 'ø' might cause panic...
Mads - not as bad as Bent but still a no.
Girls
Mette - I'm very good friends with a Mette. Everyone pronounces it Meh-ta. Getting anything closer to the Danish pronunciation is a lost cause. Also lots of spelling mistakes - Metta, Mehta, Meta, Metha - which she finds a pain.
Helle - Hell-uh would mutate into Hella I think - as for Mette the "uh" sound is not natural for English speakers. And then you have this to contend with.
Astrid - nice, would be pronounced with a hard D though.
Sofie - fine, would be pronounced like the English Sophie not So-fee-uh. Would always have to be spelt.
Maja - I think the English would have trouble pronouncing it. Their first attempt would be with a J sound like in 'juice'.
Bodil - would be pronounced "Bow-dil" or "Bodd-ill". You could try to enforce "Bore-dil" - closer to the Danish - but then the name starts with "bore" :(. Unfortunately close to 'B.O.' (body odour), 'libido' and 'dildo' - sorry to be so crude but I'm talking from experience, I know a Bodil living here and she hates her name.
Dorete - OK, again you would have to explain the last syllable needs to be pronounced, would probably turn into "Doreta" which isn't that bad.
Asta - fine.
Tbh, as a Dane living in England myself, I would try to go for a truly English name unless you live in a very multicultural area where it's common for everyone to have to explain their name. It becomes very, very wearing.
I think the jury's out on names like Sofie where they have a close English equivalent. Because your names so integral to your identity, it's quite hurtful when people get it wrong, not just acquaintances and the like, but friends. For example, the Mette I know has just received a thank you card for the hard work she's done volunteering somewhere for multiple years. They spelt her name wrong on the card - takes the gloss off it a bit. There's also the hassle of getting your name right when e.g. opening a bank account and then having to change it afterwards when the assistant hears "Sophie" and assumes s/he knows how to spell it.
There are lots of names that are common in both languages. Just looking at the boys and girls top 10... Isabella, Anna, Caroline, Emma, Sara, William, Noah, Lucas, Magnus, Victor, and Oscar could all be easily pronounced and spelt in England.