Kelly this sounds like a great idea, but already 14 courses have been mentioned.
Help us out a little. I'm guessing form the 'Sandbelt' comment this will be your first trip? (Heathland 
)
What kind of golf do you like? Short and Quirky or big and brawny?
If you want to see a selection, how long have you got?
Do you want to play links? As JNC Lyons proved, you can probably play half of George Peppers 246 links courses in the world, on a day trip from London. But it’s easy to play Royal St George’s(this year’s Open venue), Deal, Princes, Littlestone, Rye or Burnham on a day return. All fine courses.
There are also about 150 heathland courses and about1/3 of them can easily be played on a day trip from London.
MM then there’s budget. Wentworth was £225 last time I looked and I’ll never pay that but Woking for £40 is worth seven plays in a week.
So fill in a bit more info and I’m sure you’ll get some good advice, and hopefully we can meet up.
Tony
Prestwick = VERY doable in a day from London.
Seriously, though, the London Sand Belt is a great place to play golf. When I got to London, I was overwhelmed by how many courses there are in the London area that feature brilliant architecture. Basically, your choice of courses depends on how much time you have to see them.
Woking, Swinley Forest, Huntercombe (Oxfordshire, but still within the sphere of the sand belt), and Addington are all top-notch.
I would recommend Woking more than any other heathland course for a few reasons. First, the collection of greens at Woking is extraordinary, from the runaway first green, to the elevated bowl at the third, to the multi-tiered, cascading 12th, to the subtle but brilliant 4th and 17th. Woking might be my favorite set of greens in the UK. Second, Woking was a seminal course in Golden Age architecture. The 4th hole is the ultimate strategic par four that laid the groundwork for the great strategic layouts around London. Third, Woking is very accessible from London (25 minute train from Waterloo, five minute taxi ride to the course) and has a great twilight rate. I played Woking twice in the late afternoon (yes, I did play 32 holes after 3:30 one time) and enjoyed immensely. The course was empty and in great condition both times. Woking is my top pick for the London sandbelt.
Of course, you can hardly go wrong with courses like Swinley Forest and Addington, which are, incidentally, polar opposites in terms of a full golfing experience. After reading Ran's profile, I am kicking myself that I didn't see Sunningdale (New), so that should probably be high on the list as well.
Huntercombe is a real gem that gets no press. It is one of the first modern golf courses, and it is a perfect example of how a course can be great without using bunkers excessively. It changed the way I think about golf course architecture.
If you are in London, Sandwich and Deal are very convenient from Kings Cross St. Pancras. We have several Deal members on this site, and you should be able find one to host you there if you choose. It is a day trip (1.5 hours to get down there from St. Pancras), but it is more than worth it. Sandwich is a little tougher, and getting to the golf course from the train station can be tough unless you are willing to make the 30 minute walk (as I did, twice). Of course, playing the 2011 Open venue might be worth it.
In general, London is your oyster as far as golf is concerned. There are few places in the world with a denser population of great courses. It all depends on what you are looking for, I suppose.