I’m sorry but its full of mistakes, I have listed some of my findings below.
Too much plain words, we don’t use “this is”, “at”, “aircraft type”, “with”.
A correct clearance request would be:
- “Arlanda delivery, Scandinavian 123, ATR76, Stand 1, Information A, QNH 1020, IFR Copenhagen, request en-route clearance”
There are variations to the standard clearance request above depending on the airport, as an example, at Amsterdam Schiphol airport:
- Schiphol Delivery: call sign, destination, “request en-route clearance”.
- Schiphol Planner: call sign, position, ATIS, QNH, “ready”.
- Schiphol Ground: callsign, position, “request pushback / start-up”.
We don’t use terms like “pushed back from”. You are already on Gatwick ground since you requested push and start so no need to restate the position of the aircraft. If you do need to switch on ground you always call with call sign, position, request. But “pushed back from” is not something we use, rather “abeam position …” or “taxiway …”
Nooo, don’t use “with you”, this causes everyone itches and everybody instantly knows you are an American 
. When you switch frequency on ground you need to state the aircraft position, so:
- “holding point …, runway …, ready for departure”
“Taxi and hold” is NOT used anywhere in the world! Its “line-up and wait”.
Usually the other way around, first runway, then “cleared for take-off”.
Not “with you”, no “at”, example:
- “Stockholm control, Scandinavian 123, FL190, direct PETEV”.
Not “directing”, use “direct” for waypoints or “inbound” for navaids.
ATC would think, cool, good for you, what do you want? You should use: “request descent”.
NEVER use the phrase “to” in connection with flight levels. The phrase “to” is only used in connection with altitudes or heights, immediately followed by the phrase “altitude” or “height” as below:
- “Climb to altitude 3000 ft”
- “Climb flight level 390”
We don’t say “on frequency”.
- “Contact Frankfurt tower, 123.250” or “Changing to Frankfurt tower, 123.250”
You don’t get switched to tower before you are established on the approach around 4 to 6 miles, so the arrival route is no longer relevant. You don’t request landing clearance, why else would you be on approach? Information you should have called long time before on approach frequency.
- “Frankfurt tower, Scandinavian 123, Runway 25L” or “ILS 25L” is also fine.
Correct check-in with ground:
- “Frankfurt ground, Scandinavian 123, runway 25L vacated at …”
I wrote a manual about proper radiotelephony, use that instead:
Radiotelephony Manual.pdf.pln (3.7 MB)
Remove .pln from the file name after download.