Yes, British people do say "you're welcome" as a response to expressions of gratitude or thanks. Just like in many other English-speaking cultures, "you're welcome" is a polite and common way to acknowledge someone's thanks and show that their gratitude is appreciated. However, it's worth noting that British English can have some regional variations and different phrases to express politeness, so you might also hear other responses like "no problem," "not at all," "my pleasure," or "don't mention it." The context and personal preference often influence the choice of response.