Morning amcapt89
What time of day did you want to fly? How busy it is in the area you want to join is going to make a difference to your joining clearance, as you are aware. It will also make a slight difference if the prevailing conditions make it Easterlies or Westerlies at the major London airports, as you might start to mix it with traffic inbound to Luton and Heathrow looking for short cuts on an Easterly day.
However, my lovely colleagues on the North Bank in TC are just like the rest of us, and always endeavour to provide the best possible service. You will most likely get a join within minutes, and once joined should have no delay en route.
The other thing to be sure of is what your intentions and options are if by any chance you don't get a a join... would you hold and await one? Continue en-route and see if you can get a join further down (CPT?)
"In short I would like not to be in a half an hour hold over an enroute beacon because the planned flight is in the middle of the heaviest commercial network in the UK, and the controllers cannot give me any clearance."
Your flight is in the middle of the heaviest commercial network in the UK. But we're nice (Mostly !
), and will do our best to give you what you want.
Make sure your flight plan is filed, consider who you will ask for your joining clearance, who (if anyone) you will work whilst outside CAS, and what you will do if you don't get what you want.
IF you can accelerate to 300 knots and climb at 3000ft per min that'll help as well!
Have a good flight.
Cheers,
Northerner
"Keep smiling - it makes people wonder what you're up to...."