Whirly - relating to your trip (I won't start the debate on Solent, who have previously on more than one occasion kept me on standby, orbiting just inside EGHH zone, for 10's of minutes to let their single item IFR traffic depart
), attached is my 1.5p worth.
From experience,
Edinburgh have never refused me entry, but may ask for altered routings / altitudes to stay clear of IFR traffic - you may occasionally need to orbit at the zone boundary while you try to get a word in edgeways or get a progressive clearance through the zone if you want to fly through the overhead. EDI ATC are *very* helpful generally and will try to give you a 'tourist clearance' direct over the City Centre when traffic permits - that's always a good one and I always cross my fingers if anyone asks questions about Rule 5
Glasgow has never been a problem (well, on the once I've been in their airspace!).
Dundee has never been a problem (well, on the once I've been in their airspace!).
Benbecula were very helpful on the two occasions I've been in their airspace.
As gasax says, Leuchars will try to give clearance into their MATZ whenever possible, but there is is a lot of fast jet activity on some days which can give you a sore neck trying to find the traffic!!
Further South:
Carlisle were very helpful when I made a precautionary landing due wx on my way down to Sherburn. I was more or less given a 'come in any direction you want from whichever entry point you choose, land if possible on tarmac and try to give a finals call' type clearance!!
Whilst being totally certain of my position but unfamiliar with the field and not having originally planned to land there, that saved a bit of workload planning the circuit!
Newcastle were quite pleasant when I transitted alongside their zone (entry not required).
Teeside - refer to Newcastle comments.
Leeds Bradford were very helpful when I transitted their zone on my way to Sherburn, despite handling a lot of traffic.