If there is still D class availability on the LGW sector then you can buy Y tickets for them and upgrade the available sectors with your skywards miles ( if you have enough) . This is probably going to be cheaper than trying to book 2 sets of tickets DUR-DXB in Y and DXB-LGW in J.

Even with 2 sets of tickets you don't have to pick up and check in luggage at DXB provided the transit time is less than 24hrs. Just ask the staff at DUR or LGW to check the bags through to the final destination.