These flights are with Icelandair so they are full service and do not have all the added fees. Dates for links below are Nov 12-20 for Copenhagen and Dec 4-11 for Manchester. Manchester deal is for those dates only. Other dates for Copenhagen deal are Sept 24-Oct 2, Sept 3-11, Nov 5-13, Nov 13-21, Nov 19-27, and Nov 20-28. Copenhagen can get chilly so I would choose the September dates! Most flight options include an overnight layover in Iceland (extra day of vacay! See the Blue Lagoon).
Tip: Use the "Price Graph" feature in Google flights to see the varying prices by date. You can choose your length of stay and scroll through to see what prices work for you! Then book directly with the airline. Sometimes you can spend just a few dollars more to get the dates you really want.
Link to Copenhagen Flight
Link to Manchester Flight