How to get my iPhone 5 to work in the uk?

I have an iPhone 5 from tmobile I'm in the uk for vacation. How do I get it to work here do I need to purchase something cause my phone has no service at all

You probably need to set up 'roaming' with your provider. Might have been something you needed to do before you came over but there may be a setting on your phone for it.

Does your iPhone have the right documents to work in the UK?

You need to phone your service provider and set up Roaming! It should be pretty easy. But do be careful has the roaming costs are normally pretty expensive.

T-mobile where?
T-Mobile UK, Germany, US, another country? (they have different networks everywhere)

And are you using your Home country SIM card or a local UK one?

Some more information needed really.

If you are using your home country SIM,
then I expect you do not have roaming enabled OR have not agreed the extra costs of roaming (esp data costs!)

If you want to use a UK local SIM card, you need to arrange to unlock your iPhone from your home country operator (and that takes several days, money and connection to iTunes to reload/update it)

You need to contact your carrier. They will help you out with this. Hope this helps you.