Changing UK Departure Date

[caesura]

So, long story (hopefully) short, I am a bit unsure of what to do right now. I'm a US citizen visiting my s/o in the UK; my trip was orignally going to be for a month but I'd like to extend it out for a few weeks more. I don't technically have a visa because US citizens don't need them for short stays in the UK, so I just have the entry clearance stamp (which means no electornic visa application that I could just update online...). Everything I've read has suggested that the stamp should be good for up to six months, but when you go through the entry interview, they ask you for a departure date. That date gets included on that little card they have you fill out when you arrive at the border, and presumably put on file and checked against the actual date of departure from the country. I was only planning to stay for a month when I filled out that card, so I am just trying to figure out whether I need to report and/or get permission to stay longer than that. I will end up trying to call around later this week, but there isn't a huge amount of information on this on the gov.uk website, so I just thought I'd ask here in case there's anyone who may have done this before or knows anything about the procedure. Thanks in advance for any help!