Working Holidays in the UK & Work Permit regulations

[tuning-fork]

Hi Folks,
I’m non-EU national permanently resident and living in Czech Republic. My wife and I are planning to travel to the UK for holiday and I will need a visa before travelling. I was told UK visitors are usually given 6 months visa which doesn’t allow them to work in the UK. I am planning to apply for a working holiday visa instead of a visitor’s visa because I will like to work during my stay in the UK. My question is; would it be possible to obtain a working holiday visa if my Czech wife doesn’t have the intention to work during this 6 to 12 months holiday period? What are the requirements needed to apply for a working holiday visa being a national from a Commonwealth State and EU family member? I know I can get a family visa if my Czech wife lives and work in the UK; which is not the case now.

Your advice would be highly appreciated!

Best regards,