Hi, yes you can become a member from the UK. If I remember rightly you can't use Disney financing if buying direct unless your actually in Florida to sign for it.
If you get in touch with DVC member services they will send you out all the brochures and details, this gives you a chance to familiarize yourself with all of it. Bear in mind that they will only try to sell you the resorts they are currently marketing- which I think are Animal Kingdom Villas and Grand Floridian Villas. If another resort is what you want they normally have them available to sell but will really push the other 2 resorts.
Also as another thing to consider have a look into the resale market, you can get the same amount of points for half the money doing resale over direct. Something we learn't the hard way! Although we are very happy with our purchase so in the end thats all that matters.
Please make sure you understand that you automatically lose 10% of your DVC resale value at resale due to FIRPTA law. You may recover that tax if you choose to file an American tax return with IRS even though you are from UK. Most dealers will not warn you so your $80 per point needs to be sold at $100 to just break even due to this tax and commission.