My wife and I are travelling to the UK in about 4 weeks. We will be there for about 8 days. What are the must see places?

Depends on where in the UK... You realize that the UK consists of several countires (Northern Ireleand, England, Scotland, Wales), so what area are you going to visit?  

I'd say that 8 days is enough time to see one or two spots, but not more than that if you want to really enjoy it.

So for starters, Oxford is a nice place to grab a beer and relax, and eat some delicious meat filled pie at the Eagle and Child pub.
Stonehenge, while touristy, is also worth seeing, just for the awe of standing there in something that predates modern history.

There are a LOT of small villages and towns that have amazing cathedrals if that's your thing.

London is just too big to even start on, really, so touristy things:

Big Ben, London Bridge, Eye of London, Westminster Cathedral, etc.

English pubs are ALWAYS great for beer and dinner and you will find them everywhere, and each one is a bit different.

London has some of the best Indian and Middle Eastern food outside of those areas as well.

Dublin has more of the same, plus a Guinness factory, a whisky store and canals, lots of history.

Don't take taxis unless you really need to, they're ridiculously expensive in London (all over Europe in general). Take the Tube and buy an Oyster Card (at the Underground station at Heathrow).  

Dont forget to visit the mosques. Theyll love ya

I don't know about Middle Eastern food, Put Pork Curry is some AWESOME SHIT!!   Pork any other way to me now sucks.

Go north.

Edinburgh Castle.

Imperial War Museum then GTFO out of London.

I would go to the Isle of Wight and then the Isle of Man.  

British museum.
Definitely the Imperial War Museum.  Cabinet war rooms, Tower of London.
Hadrian's Wall.  The gun shop in Inverness.

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Go to the RAF Museum in London; I went to days in a row to ensure I saw everything.  There's a Vulcan bomber with the bombay doors wide open; you could part a bus in there...

There are a lot of things to see in London. You could take a much longer trip, stay there only, and not get the full taste.

I would visit the British Museum first. It is an incredible collection. The Imperial War Museum is excellent, and The Tower of London. Hampton Court is a palace that Henry VIII built for Cardinal Woolsey and confiscated when he tired of the Roman Catholic Church. The palace has tours and is an outstanding example of period living.

I wanted to go to Stonehenge both times I went. My mother first, and then my girlfriend, dismissed it as "a pile of rocks."

I'd be tempted to visit Bath, or Hadrian's Wall, and probably go to Bath for the old, Roman stuff.

Start learning the train schedules. You can do a lot with the trains in the U.K. Save yourself some driving and enjoy the trip.