For your question about which government rule relates to your case, the answer is Paragraph 46G of the Immigration Rules. 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 where you can read more on how the rules are interpreted.

Update from 20 March 2015

Bowing to pressure from advocacy groups, the Home Office has reversed a policy. Accordingly this answer needs an amendment... Holders of a Business Visitor Visa who received their visa prior to 24 April 2015 can perform ANY permitted activity under the new regime. Namely...

People who hold a valid visit visa that was issued prior to 24 April 2015 can use this to enter the UK provided they are still a genuine visitor.

They will be able to use this visa to carry out the additional permitted activities. For example, a person with a business visit visa can use this to enter the UK for a holiday or to receive private medical treatment.

Source: email from the Home Office to stakeholders sent on 20 March 2015 (today)

As always when rules or policies change, carry a print-out with you. Not all line staff are in the same tranche for training.