Is it OK to use pedestrian phase of pedestrian crossing to join/leave the carriageway? (UK)
I doubt the Police would stop you for doing so if you're not causing a nuisance or danger to pedestrians or other road users. I've seen it done plenty of times by cyclists and done it myself.

The Highway Code rules that apply to this are: 

Rule 64:
You MUST NOT cycle on a pavement.

Rule 79:
Do not ride across equestrian crossings, as they are for horse riders only. Do not ride across a pelican, puffin or zebra crossing. Dismount and wheel your cycle across.

At the start you should wheel your bike on to the road and start riding. If you're not on the crossing you are just taking advantage of stationary traffic.

At the end, you are allowed to get off your bike and wheel it across or onto the crossing. Pedestrians regularly enter crossings from the carriageway. Just make sure you have time to do so.