This one is very expensive.
The most cost effective way is Kings Cross to York return.
http://tickets.eastcoast.co.uk/ec/en/JourneyPlanning/MixingDeckThe 8.12 and 19.02 were £27.20 return when I booked 15 minutes ago but as you can see have gone up already on the outward leg.
If you do a search for London to Middlesbrough it works out at approximately £68 without a railcard discount.
York to Middlesbrough return is £12.30, again without railcard, this seems bookable on the day
Comments
http://ojp.nationalrail.co.uk/service/timesandfares/London/YRK/270413/1004/dep/270413/1830/dep