I've used the Low Level Route on both occasions I've been to Barton, and been in contact with Manc Appr the 1st time only.
It was so busy it took me ages to get a call in to request freq change to Barton, & I ended up orbiting very close to Barton's ATZ & Manc CTR, not very enjoyable, in fact thinking back it was probably my most unpleasant moment in aviation.
Even if you get a hand off as you exit the LLR, it's only a 5 min flight to Barton, not much time to get your call in & get orientated before the overhead.
The 2nd time I didn't speak to Manc (although I listened out on freq), and called up Barton when half way up the LLR. Plenty of time to get organised for the overhead join - much easier IMHO