You can plane one face reasonably flat by hand (not perfectly flat all over but sufficiently flat so that it doesn't rock) then flip it over and pass it through a "lunch box" thicknesser such as one of these,
http://www.axminster.co.uk/jet-jwp-12-b ... hicknesser
Take a few light cuts (say 0.5mm or 0.75mm) until the second face is flat, flip it back over and bring the first face down to perfectly flat, then keep flipping it back and forth as you bring it down to finished thickness. It's not the perfect system (that costs well north of £1,000), but it works. I did it for several years when money and space were tight and produced a lot of hardwood furniture that I'm still very happy with.
The workshop where I trained didn't have electricity until the 1960's, and they still managed to produce furniture that today commands tens or even hundreds of thousands of pounds at auction. The trick is to be realistic about the projects you undertake, using this approach to build a sixty foot ketch or a Carlton House Desk in Macassar Ebony is probably a step too far for a hobbyist. But modestly sized furniture in reasonably forgiving hardwoods like Elm or American Cherry is perfectly do-able.
Good luck!