There are direct trains from St Pancras (next door to Kings Cross) to Carshalton. Alertantively, get the tube to Victoria, then a train service from there.
Unfortunately, on that day, there are no trains from Boston direct to Grantham (normal change station for London). However, on the way down, if you get the 7.46am from Boston, you can change at Sleaford for Peterborough then go to London from there. There's no way of avoiding the bus replacement on the way back - making you go to Peterborough, then a bus to Grantham, bus to Bottesford, then train to Boston.
