Living in Denmark, employed in Sweden, working in England?

Dear Tax people at Skatter.se

First of all, feel free to to answer in Swedish, as I can read Swedish but not write Swedish!

My big question is what will happen to my taxes in the near future? Currently I am employed at Lund University by living in Copenhagen, therefore  I am intitled to pay SINK skat (25% flat rate tax). However, in the near future, I will be moving to England with my girlfriend and hopefully start wokring at a university in England, but still get my salary paid from Sweden. 

I guess the Danish tax office will not have any interest in my income once I am out of the country? However, will this result in a cancellation of the SINK agreement? Or is there similar treaties with England? Will I have to pay full tax in Sweden and no tax in England, or?

In addition to this I have a minor income from renting out a property I own (Currenly also pay of mortgage for this property).

I would be sincerely thankfull for any comments or answers to my questions, please feel free to answer in Swedish.

Thank you,

LH