Mesmo, Turkey is not a member of the Schengen Zone.
Both you and your wife will need to secure a tourist visa if Turkey is your choice.
Here's a good resource that shows all the countries that Philippine citizens can visit without visa - Visa Requirements for Filipino Citizens
Here's another good resource with visa requirements for both UK Citizens and also for Filipino Citizens
If you wish to visit a country where a visa is required then first stop on how to apply would be to visit the specific website of their Embassy in UK
Good luck![]()