You do get one 'outbound' and one 'inbound' day in your country, so you could travel to London on the train and then get the Eurostar on the same day, but you can't stop overnight in London as then the Eurostar would be on the second day.
In fact if you're coming from the North East it can be beneficial to pay the extra for the first class pass if it's not prohibitive. You get first class travel to London (including food on the LNER) and then can book the Eurostar for (I think still) £38 supplement each way which gets you into Standard Premier, rather than £30 for standard class with the 2nd class pass.