Usually the currency exchange rate between two countries tells a lot about their relative economic performance. Ofcourse managed currency like Indian Rupee is an exception to this. Nonetheless, the consistent and sharp downfall of UK Sterling pound against the US Dollar is merely one indication of the fact that the recession in UK is probably worse than in US.
What started as an economic problem of US, has grown to be a bigger problem for other countries like UK. Here are some related news articles.
BBC: UK Economic downturn 'frightening':
Business leaders have painted a bleak picture of the UK economy, with a survey suggesting the end of 2008 saw a "frightening deterioration".
NDTV: UK vehicle production collapses
The Society of Motor Manufacturers and Traders, or SMMT, said nearly 48 percent fewer cars were made in December 2008 compared with the previous year, meaning that in 2008 as a whole car production dropped by almost six percent. In addition, the group said commercial vehicle production fell about 57 percent in December from the previous year, with full year production down six percent.
Currently US national debt is about 60% of US GDP and UK national debt is about 44% of UK GDP. Note that national debt is merely one indicator of economic situation, and on its own does not provide a fair comparison of economies. The currency exchange rate is perhaps a better indicator. Another thing to remember is that the currency exchange rate only serves as a comparison of economies from a very short term viewpoint. That is the reason for the question mark in the title.