I am holding a valid UK business visa and have visited UK for business purposes on prior visits. Am I allowed to enter UK with the same (business) visa if I am travelling to UK for leisure now?
There are two sides to this question...
If you are in the UK on a business visa, and you want to add some time for recreation and you can demonstrate that it is not the principal part of your visit, it is ok. It's reasonable for an individual to spend time in that way and no one will object.
If you are outside of the UK with unspent leave on your business visa and you want to engage solely in a tourist visit, it falls within the cognizance of the Immigration Officer to allow or disallow; it's spelled out in Paragraph 46HI of the Immigration Rules. This is because you want to do something different that what your visa was issued for. However, if you provide a satisfactory explanation to the IO, you will not have a problem. There is no way to tell the outcome in advance for a situation that falls within the discretion of an IO.
In all cases, you are bound by Paragraphs 41 of the Immigration Rules for any tourist/recreation activities you undertake.
A lot of people have this question and UKVI will be updating their web guidance early this year so as to leave no doubt on mixing business and recreation. This answer is consistent with their guidance.