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You are in a long-distance relationship and want to visit for 6 months. You also want to avoid any discomfort in your landing interview by lying to the Immigration Officer about the length of your visit. So is this OK?
Internet couples try this all the time and some succeed, some do not. A single woman from 10 time zones away queueing up at immigration wanting to stay for a week or so is a dead-giveaway. How good are you at landing interviews? If the IO suspects something is amiss they will probe and try to trip you up; if you are caught out, you will be removed from port (that's a bad thing). You can read in our archives where this happened to people in your situation.
But paradoxically, it's worse if you succeed. It means thereafter you will have to perpetuate the lie if you get married or engaged or study or work permit or any other situation that requires a Singaporean to obtain an entry clearance. Let's look at the form...
Lying on an entry clearance application is covered in Paragraph 320 and attracts a 10 year ban. Your exit details are provided to UKVI by the airline.
So our response here on Travel.StackExchange.Com is strictly party line: tell the truth to the Immigration Officer. If you want to be pre-approved for your visit and avoid the distress of wasted airfares and removal from port, then you can open an account at visa4UK and apply for a Standard Visit Visa. It's fine to explain to them that you are in an LDR and applying in order to avoid the distress, etc etc. They have seen it all before.
Notes: the seminal analysis of decision making by immigration officers is "Exploring the decision making of Immigration Officers: a research study examining non-EEA passenger stops and refusals at UK ports" which was commissioned by the Home Office in 2007.