A couple of early votes for Newark, but the current service actually crossing over the ECML is only one passenger one per hour (generally a two coach DMU) plus a very small amount of daytime freight. Yes, a flying junction would permit more passenger services, but we have enough problems dealing with the practicalities of congestion at existing bottlenecks before we have money to spend on the "if you build it they will come" stuff.
Down south, Woking and Didcot both seem good shouts to me - give how busy existing lines are and how many passengers per hour are potentially inconvenienced by such bottlenecks.
North of the border, Hyndland East would be a good one to fix (probably the most pressing one in the UK), maybe the flat crossing at Motherwell too?
North of England, I'm wondering about Doncaster. There are currently three passenger services per hour from the Conisbrough line to the Kirk Sandall line (Sheffield to Hull, Scunthorpe, Cleethorpes), so six services crossing the ECML on the flat. Now that so few of the Scottish services stop at Doncaster, it probably affects how easy it is to schedule "Provincial" services crossing between "InterCity" services. Maybe something south of Manchester Piccadilly to sort out the Airport/Stockport split at Slade Lane?