A season ticket from Grantham to Kings Cross is £206.60 for a week. An annual season ticket is normally 40 times the price of a weekly, which works out at a weekly rate of about £160. An anytime return from Grantham to Kings X is £120, although you could reduce that to £79.20 if you have a 16-25 railcard.
If you know well in advance when you are likely to be travelling into London, it may be possible to save money by buying Advance tickets, which are valid only on the train specified at the time of booking (but can be rebooked for a different time/day by paying a £10 admin fee and any increase in price since you booked). For the direct trains, that may not save anything if you are trying to book only a few days ahead (and in the mornings there may not be availability).
What does seem to be available, e.g. I looked at travel on Wednesday (i.e. 2 days ahead), is Advance tickets valid on a specified train from Grantham to Peterborough and then on any Great Northern train to Kings X (or in the evenings, on a specified train from Peterborough to Grantham, and on any connecting Great Northern train from Kings X to Peterborough). That will increase the journey (effectively from just over an hour to just under 2 hours), but for 2 days ahead the fares were from £16.15 for one way. But doing it this way will involve a lot of time booking and collecting and keeping track of tickets.
As for the onward travel on the Underground from Kings X to SE1, it may be that for 2 or 3 days per week, paying £2.30 per single journey using Oyster/contactless "pay as you go" will be cheaper than buying a season ticket that also includes full use of underground/buses/docklands light railway throughout zones 1 to 6. Which will be the nearest tube/DLR station to your destination? Also, would it help to get a train that ends up not at Kings X but at Moorgate?