Kings Cross and Hitchin have been reduced in size and the work moved to new traincrew depots at Hornsey and Welwyn Garden City. There is a waiting list for moves to Kings Cross and Hitchin of displaced drivers so no one external will be going to either of those two any time soon. Peterborough also has about 20 drivers on the waiting list, so no one external will be going there any time soon either.
Hornsey and Welwyn Garden City will be your best chance of vacancies popping up, and surprisingly Cambridge does have vacancies sometimes too.
Recruitment has been "paused" for the moment, but there is still plenty of training to be done for drivers to learn ATO in the Core, and an increase in services planned, so keep an eye out on their website, and sign up for job alerts:
https://gtrailwaycareers.com/jobs
(Just in case you are thinking, "Maybe I could drive to Bedford traincrew depot," Bedford was also reduced in size, with new train crew depots opening at Luton, St Albans, and Cricklewood, and there are a staggering FIFTY drivers on the waiting list to move back to Bedford, so no chance of getting in there for the foreseeable future either I'm afraid.)
LNER have a train crew depot at Kings Cross, keep a lookout here regularly, and sign up for job alerts. There is to be an increase in service in the next few years.
https://lnerjobs.co.uk/jobs/
Greater Anglia have a train crew depot at Cambridge, again keep checking their website frequently as well as signing up for job alerts.
https://careers.greateranglia.co.uk/vacancies
Cross Country have a train crew depot at Cambridge, but only seem to take on qualified drivers infrequently.