Generally speaking, the UK is a very safe country. Crime rates appear to be on a downwards trend and there are dozens of county police forces that are working hard to bring these statistics down even lower.
In the majority of cities, towns and rural areas you will feel and be completely safe. The majority of hotels in the UK are very security conscious and crime is extremely rare in these circumstances.
There are a few basic precautions that you should take, however. There are some parts of London and other major cities (e.g. the largest northern cities, Glasgow, Birmingham and Bristol) that are noted for higher rates of crime.
You must use your initiative here and ensure that you keep your purses and wallets safe at all times. Do not flaunt large amounts of money in any areas and make sure you keep your PIN number concealed when using ATM machines.
Some areas where there are high concentrations of pubs and nightclubs will appear as quite intimidating places at night. Try to avoid these if you possibly can. Unfortunately, there are high levels of alcohol-related crimes in most urban areas.