1 - no transponder, hence no TCAS protection.
The last time I remember flying in London, transponders were not required in uncontrolled airspace under the TMA. So you won't get any TCAS protection if someone busts vertically anyway.
2- no good reason to enter CTR
You may want to enter terminal airspace to save time and fuel on your journey. You also let the controller know who you are and what you want to do. They will also give you a route to operate safely so nobody is panicking if you bust.