You should refer to the HMRC helpsheet HS275
as part of this answer.
You can only claim entrepreneurs' relief if you are reducing your capital involvement in the business. In the case of a limited company, that means selling some or all of your shares. That is not what is happening in your case. The company owns the business goodwill and that is what you are looking to sell a part of, ie something owned by the company.
Give that there are two parts to your business and that you want to retain one part, you would need to find a way of separating them. The problem you have is that if you split the business into two companies, there may be tax consequences which I cannot go into here (see here
) and which you would need to take much more detailed advice on before going ahead to avoid the pitfalls.
However, take a look at the article here
. This suggests that a properly organised demerger resulting in two companies could allow you to sell your shares in the water cooler business and claim entrepreneur's relief even though it may not have operated as a stand alone trading company and you not may not have held the new company shares for 12 months leading up to the disposal. There is the potential for HMRC to claim that tax avoidance was the reason for the demerger as opposed to genuine commercial reasons.
I hope this helps but let me know if you have any further questions.