Upvote:4
You are a permanent resident of the US, but (unless you're stateless) you remain a citizen of the country from which you emigrated, the Philippines, and (unless you're a refugee or stateless) must continue to carry and renew your Philippine passport for travel purposes. If you naturalize as a US citizen, then you can apply for a US passport and use that for travel.
As such, you will need to enter the UK on your existing Philippine passport, and because you require a UK visa for that visit, you will need to obtain the visa before you travel.
Your US immigrant visa is irrelevant. Its only use is for you to travel once to the US and obtain your permanent residence. After you have your green card, the immigrant visa has no other use. In particular, the UK is a completely different country than the US, and a US visa is not valid for entry into the UK. The only thing a US immigrant visa may allow you to do in the UK is transit landside without a visa, but your green card is also good for this.
The green card does have some travel benefits, though. For instance, you can transit without a visa in some countries that would otherwise require you to obtain an airside transit visa (or in a very few cases, allow landside transit). You can also visit Canada or Mexican border areas without a visa. You should carry both your passport and green card when traveling, to take full advantage of these.
In short, your immigrant visa has no purpose anymore. You need to renew your passport in order to travel. And you need a valid UK visa in order to visit the UK.