UK people, is UK dependent on US, as Rachel Reeves say she has to put taxes up because UK economy has suffered due to imports to US?

As of today, Rachel Reeves has made no statement about putting up taxes for whatever reason. Lots of people are commenting that she's preparing the way for doing that, but at the moment that's all speculation and worth little.

As to your question the UK is a trading nation and is dependent on being able to do trade around the world. The US is one of the important countries which it seeks to do trade with.