Go to Dover first, then stop off on your way back to London at Canterbury. You can do this on a off-peak return London-Dover costing £22.65. You can't do this in reverse, ie stopping off on the way to Dover as you can only break your journey on the return leg.
You don't say where you are staying in London; you can get to Dover from Victoria, Waterloo East / London Bridge on the above fare. High speed from St Pancreas would be £26.40.
If you want to do Dover as a day trip from a base in Canterbury, buy an off peak return London to Canterbury (£19.20 - non high speed, £22.95 with HS) and then a off peak return from Canterbury East to Dover for £8.10.
Avoid buying single tickets in general as returns are usually priced at a little more - day returns often are only 5p or 10p more.
If you were trying to pack this all into one day, a off peak day return London to Dover is £25.55 including HS.
There are no advance tickets on these routes.