I don't know what I need to do for travelling to UK because the law in UK is different from US. I'm asking if I can still travel to UK since that I have only Philippines passport and my US immigrant visa is already expired since 2012. But I am immigrant and a permanent residents in US. I have green card which is still valid and my problem is would i need to renew my Immigrant visa just to visit UK or is there any possible that I can still travel to UK, if I only renew my passport not my Immigrant visa? Would I need to renew both of them so I can visit UK? Or would they let me to enter in UK without/with UK visa? Would they let me to enter in UK with renewing philippine passport and not renewing my Immigrant visa for US? How much the total cost of an immigrant visa fee and passport? Is it alright if i only renew the passport but can i still visit UK without renewing the immigrant visa? what do i need to do?
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.