Provided that you are willing to be a bit flexible if needed then no reason that you would be refused transit, I cannot remember the last time I could not get someone through the eastern stub unless the R/T was almost unreadable!
if we have inbounds ie on 27 then normally vfr not above 2000 will be OK routing wymeswold or just east I will run the ILS traffic across the top and descend clear with traffic info-if WX is less than good then down the M1 just east of the field is another way through-the point being that you may have to accept a height limitation or restrictive route(hopefully not both!)
plent of people at sherburn do it on a regular basis