BLACKPOOL, England — The woman on the other end of the phone spoke lightheartedly of spring and of her 81st birthday the previous week. “Who did you celebrate with, Beryl?” asked Alison, whose job was to offer a kind ear. “No one, I…” And with that, Beryl’s cheer turned to despair. Her voice began to quaver as she acknowledged that she had been alone at home not just on her birthday, but for days and days. The telephone conversation was the first time she had spoken in more than a week. About 10,000 similar calls come in weekly to an unassuming office building in this seaside town at the northwest reaches of England, which houses The Silver Line Helpline, a 24-hour call center for older adults seeking to fill a basic need: contact with other people.