Will the US IPhone 6 work on SK Telecom (KR) and Tesco Mobile (UK)?

There are no unlocked iPhone 6 models currently for sale in the US.

When unlocked models do come available (Apple has not yet announced

when this might be), warranty will be valid only in the US and 4G/LTE will

not work in Korea or UK.

Actually imobi is technically wrong

All the US iphone 6 and 6+ models have the capability to support Korean bands 3 and 8 plus band 20 used in the UK by O2 (Tesco mobile are a Mobile Virtual Network Operator - acronym MVNO and use O2's network) however Apple has yet to price or offer Unlocked iPhone 6 and 6+ models to the market.

Currently US models are all network locked even the contract free T-Mobile US model as far as we know.

That said there are many hurdles to achieve what you are asking even when unlocked phones become available and actually a UK phone may be better for you if a bit more expensive up front, as all UK carriers are obliged to offer unlocking (may charge a fee) and they support the LTE bands your require.

If the UK is your primarily abode you really should consider that extra cost as warranty guarantee as you won't get any support even for a fee from Apple if your US phone breaks here.

A further problem to overcome is that many carriers are monetising access to LTE/4G services over above 3G via contract and blocking methods meaning that you may just end up with 3G access on a pay as you go sim card.