For your question about which government rule relates to your case, the answer is [Paragraph 46G of the Immigration Rules][1].  And specifically sub paragraph (iii)...

> intends to do one or more of the following during his visit:

Based upon what you wrote, you have accomplished one or more of those things and you now propose to use your entry clearance for tourism.

It's true that they will **tolerate** tourism as **part** of a business visit as long as it is **incidental**. But you would be making separate visits for separate purposes so it's hard to see how the justification can be made.  Moreover, you cannot switch out of a Business Visitor Visa into a General Visitor Visa; it was part of the conditions you (implicitly) agreed to when it was issued.

Consequently, your concern about being bounced at the airport is genuine.

On the bright side, however, the Business Visitor Visa will be abolished on 24 April 2015 and merged into the new Visitor (standard) Visa.  This means that you will not be encumbered by the restrictions of Paragraph 46G in the future (although there will be different restrictions).  You will not be able to use your existing visa to switch into the new Visitor (standard) Visa.

In addition to the rule link I gave, there's also [caseworker guidance published here][2] where you can read more on how the rules are interpreted. 


  [1]: https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/412242/Immigration_Rules_-_Part_2.pdf
  [2]: https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/371601/Business_visitors_v11_Ext.pdf