As Norman says, National Express is probably cheapest but there's only one bus per day. You'd have to travel out (from Victoria Coach Station) at 1130 on Saturday, so you wouldn't arrive until 1600. The return coach leaves Boston at 1140 on Sunday, arriving at VCS at 1620. The fare is �25.
http://www.nationalexpress.com
The cheapest rail option would seem to be to take the 0753, 0815 or 0955 departure from Kings Cross. These are all currently priced at �20.50 single. On Sunday, you could choose between the 1948 service and the one at 2117. These are both currently priced at �21, giving a total return fare of �41.50. However, you should book fairly soon as these advance fares often sell out quite quickly.
http://www.nationalrail.co.uk
Chris