Types of traction worked, as well as routes signed, are on the certificate that has to be carried at all times by drivers working to the TDLC regs, 2010. This isn't compulsory for existing domestic drivers who qualified before late Oct 2013, but is for those who instruct or assess them. Along with the certificate goes the licence issued by the ORR which looks a lot like a DVLA driving licence, being a plastic ID card with certain info shown. TDLC regs become compulsory for all existing drivers by Oct 2018. The main difference most drivers will see are a proper licence, not just a laminated bit of card, a change to competency management procedures, and more frequent medicals (every three years instead of every five). The licence can be suspended by the ORR in certain circumstances (eg long term sickness) and then reinstated, or revoked if there is no possibility of a driver undertaking main line duties again (eg permanent debilitating medical condition falling foul of occupational health standards).
If a driver moves company then the licence goes with them, it is a licence issued to the individual driver by an independent body (the ORR) and isn't property of the TOC as a SCWID (Safety Critical Work ID) or equivalent card is, for those drivers not yet working to TDLC regs. As far as the certificate is concerned, IIRC a copy of it can be taken by the driver when moving company but the original possibly does belong to the TOC. I would have to check that. Type TDLCR into your favourite search engine and the meaty PDF that comes up will answer your questions.
If a driver moves company then the licence goes with them, it is a licence issued to the individual driver by an independent body (the ORR) and isn't property of the TOC as a SCWID (Safety Critical Work ID) or equivalent card is, for those drivers not yet working to TDLC regs. As far as the certificate is concerned, IIRC a copy of it can be taken by the driver when moving company but the original possibly does belong to the TOC. I would have to check that. Type TDLCR into your favourite search engine and the meaty PDF that comes up will answer your questions.