No, being a UK resident does not grant you the right to work (or even simply live without working) in Germany (see also http://expatriates.stackexchange.com/questions/2971/does-a-non-eu-citizen-residing-in-one-eu-country-need-to-apply-for-a-visa-to-mov). The EU freedom of movement applies mostly to EU citizens and only indirectly to non-EU citizens. So what happens in German will depend on your wife's status and citizenship: 

* If your wife is a UK citizen, *her* freedom of movement rights will grant *you* the right to work in Germany as soon as she works there. You will however need to apply for a German residence card, which should be free of charge.
* If your wife is not a UK citizen, EU law does not generally apply but it should still be possible to get a spouse visa in Germany, under the conditions set by German law (within the boundaries defined by [directive 2003/86/EC](http://europa.eu/legislation_summaries/justice_freedom_security/free_movement_of_persons_asylum_immigration/l33118_en.htm)).
* (I assume your wife is not a German citizen, otherwise you would presumably hold an EEA family permit or UK residence card instead of a spouse visa)

The difference is important because [there are complex rules and additional requirements](http://www.bamf.de/EN/Migration/EhepartnerFamilie/ehepartnerfamilie-node.html) for partners of third-country (i.e. not EU) nationals. You will also need to obtain this visa *before* entering the country (as a citizen of Singapore, you can visit for a short time without visa but you are generally not allowed to apply for a residence title from within Germany). I think that whether you have the right to work depends on the status of your “sponsor” but if your wife comes to Germany to work, then you should be allowed to work too.

Finally, [directive 2003/109/EC](http://europa.eu/legislation_summaries/justice_freedom_security/free_movement_of_persons_asylum_immigration/l23034_en.htm) grants some additional rights to *permanent* residents in the EU. I don't know if it applies to your situation but in any case, it's only supposed to facilitate the process, you still need to apply for a German residence permit in this case.