I'm a natural born US citizen and wanted to live abroad preferably in the UK. If I became a citizen in the UK, would I lose my citizenship here?
You can do that. The UK does not require you to renounce your old citizenship to naturalize there, and your US citizenship cannot be revoked against your will. Naturalizing in a foreign country can result in loss of US citizenship, but only if you naturalized intending to lose your citizenship, and the State Department presumes that you didn't want to lose it (so you don't need to submit anything to the US government in advance to document that you wanted to keep your citizenship).
Loss of citizenship by native-born citizens is describes in 8 USC 1481, specifically
(a) A person who is a national of the United States whether by birth or naturalization, shall lose his nationality by voluntarily performing any of the following acts with the intention of relinquishing United States nationality...
The first thing mentioned is
(1) obtaining naturalization in a foreign state upon his own application or upon an application filed by a duly authorized agent, after having attained the age of eighteen years;
(it also includes taking an oath of allegiance to a foreign state, serving in a foreign army with some low-level exceptions, or accepting employment in the government of a foreign state, formally renouncing citizenship, committing treason).
The part of the code that I put in bold is essential. It essentially means that you have to actually renounce your citizenship, rather than just take citizenship in another country (as might be required for employment purposes).