Yes, business travel can be conducted safely, however it is important to consider the risks and manage accordingly. The threat of crime varies from city to city e.g. London has a serious issue with knife crime. Many incidents are caused by young criminal gangs or internal city conflicts, but some have also been a result of islamic extremists.
Also worth noting about travel within the UK is the heavy traffic and congestion. It is not uncommon to be sat in traffic for hours and only move a short distance. If you are in the region for business then it is worth considering secure transport for your meetings.