Deception to an immigration officer in an attempt to obtain leave to enter (regardless of whether it was successful or not) can result in a one-year ban from (re-)entry to the UK. Deception on a visa application can result in a ten-year ban from (re-)entry to the UK.

If the travel is in the other direction, entering the USA, the penalty for "misrepresentation" is a lifetime bar.

Yes, there are potentially waivers available, but lying to border agents -- and getting caught -- can make your future travel plans range from very difficult to impossible.