The only ATC units en route who will have your IFR flight plan will be Departure and Arrival airports, Scottish ATCC and London ATCC (for the purposes of your transit of Controlled Airspace) and, depending if you will be flying above FL100, Scottish & London Military.
I am not familiar with Scottish airspace, but if you are transitting at F100 or above for the majority of your route, there's a good chance that Scottish and then London Military will give you a radar service from F100 upward, but it is entirely subject to their traffic and staffing levels.
If they do take you on, you can expect to stay with them all the way until about 30 - 40nm north of Norwich, then it'll be the delights of Norwich Radar for you Sir!
If the military can't take you, or if you are flying lower, once you finish with the Jocks you should get a seamless set of handovers thus:
Newcastle - Teesside - Humberside - possibly Coningsby but more likely a direct handover to Norwich.
London Mil offer a great service (including crossings of CAS) and will see you all the way from Newcastle to the Wash so it's worth planning to fly high if you can.