Normally the visitor visa allows the holder to enter and leave the UK as many times as they'd like during the validity of the visitor visa.
The ECO would need a compelling reason to limit a visit visa to single entry and additionally would need to seek approval for such limitation from the ECM.
If you take a look at the application form you'll see that visit visas can be applied for on the validity basis of, 1 year, 2 years, 5 years or 10 years. Regardless of duration of validity though, the holder cannot stay in the UK longer than 6 months per visit.

There are a number of destinations where holders of Philippine passports are not required to hold an entry visa.
Here is a useful resource showing the Visa requirements for Filipino citizens worldwide on a single page.

Here's another very good resource for visa information. and it can be used for citizens of all countries.

Just input to the drop-down menu's

Don't forget that if you're planning to visit the EU you'll first need to secure a schenghen visa. This will need to be applied for from within the Philippines as it will not be issued from within UK to anyone with less than a 6 months visa.

Hope that helps