I'am having difficulty thinking of any economical way of doing this. Firstly you need to address the woodworm, and that includes the joists below the floorboards. The joists in a house of that age will likely be 16 inches apart so extra joists will be required as well as noggings appropriately spaced. You could have the 2x2 machined with a tounge and grove all round then secret nailed to fix to the floor. Your concept is good enough but its the execution of it which is difficult. What was though of as an inexpensive floor could end up very expensive. Ply wood is fairly soft and easly marked so it would require a high quality hard coating.
Thankyou for your reply; that's extremely helpful. We didn't look to doing this as a way of saving money, more for the aesthetic value, when laid well it is incredibly beautiful and minimalist. The woodworm has been addressed, joists have been replaced and none of the woodworm is live now thankfully. We asked only on where to buy plywood for the best price as our local merchants that we would ordinarily buy from have obviously placed a premium on this product; given that they sell so little of it. Having the boards machined is probably the best idea, I'll see who can be found to do this near us. In terms of coating, any suggestions would be welcome. A diamond hard type varnish is what we had looked to using; how effective this would be I'm not sure.
Coatings would not my specialty, but I would have thought several coats of good polyurethane varnish would do the job, i'am sure someone will be along to advise more on that. As for where to buy well i'am a long way from you, although take a look at mifi's link above.
It's a pleasure, Just trying to help. Think you have a idea in your head of what you want but doesn't sound practical to me. But what do I know.
Thinking more on this. If your doing checker board effect you would need to work out which sides require tongue's a which require groves, and also if you wish the finish to be 2x2 the board needs cut to be bigger to allow for the machining. If your fitting on top of existing flooring you could use wood flooring adhesive, and fit as per normal wood flooring. What you want to do is bit different from the norm (but could look well) and might well inspire others, but your comments to some members was bit unwarranted. Its nice to be nice, especially when looking advice from some of the most experienced people in the industry.
Quality this thread cracked me up Also think your idea could possibly look great I guess I would just ply and then glue the ply tiles to that Pretty strait forward ain't it? Other than sorting the wood worm out I would probably bevel the tiles would look awesome then make sure to share some pics would be interested in how this looks finished!