There rarely much to be gained by 'splitting' tickets on that journey, unless you are close to the date of travel and there just happens to still be some 'cheap' tickets for, say, Newcastle to Peterborough and also for Peterborough to Kings Cross, while the corresponding 'cheap' tickets from N'cle to KX have all gone.
But having a quick look at the available fares on that weekend, I can still see availability of £40 'advance' tickets for both parts of the journey.
e.g. Sat 18th June. Dep NCL at 6:30 Arr KGX at 9:42 £40.00
and Sun 19th June. Dep KGX at 10:03 Arr NCL at 13:22 £40.00
I'm assuming that :
1. neither of you have a Railcard, and
2. that by "but flexible" you mean that YOU can be flexible to suit an inflexible ticket, and not that the ticket must be flexible to suit your fixed needs on the day.