Sir George and Lady Joan Bailey are distant relations of Maud Bailey and even more distant relations of Christabel LaMotte. Sir George is a direct descendant of the Sir George Bailey who married Christabel's sister, Sophie, and who raised the daughter that Christabel conceived with Randolph Henry Ash.
Sir George and Lady Joan are the current owners and occupants of Seal Court, which is falling into disrepair. It's clear that the Baileys don't have enough money to keep the house up properly, though it's not like they're paupers, either.
As a result of their (relative) poverty, Sir George is cranky and curmudgeonly and has a tendency to protect his solitude by brandishing a shotgun. As Lady Bailey tells Roland: "George is so ashamed of the way we live—skimping and saving—the house and grounds eat money, just preventing deterioration and decay. He doesn't like people to come and see how things are" (8.113). Lady Bailey, on the other hand, is warm and kind, and she loves "having someone to talk to" (8.113).
Throughout most of Possession, we readers are led to believe that Sir George and Lady Bailey are the rightful owners of the Ash-LaMotte correspondence, since it was discovered on their property, in the room that Christabel LaMotte once occupied. By the end of the novel, we know that Maud is probably the real owner, but it's likely that she and Sir George—and their lawyers—are going to have to find some way of settling the matter fairly.