1. I'm afraid a 50p coin isn't much use as a measure. We need an accurate diameter to advise properly. Clean the paint off down to bare copper and measure the diameter. Either use a vernier caliper if you have one, or measure the circumference and calculate the diameter. Wrap a strip of paper round the cleaned pipe, and fold it sharply at a single circumference. Measure the distance between the two folds, and divide by 3.142 to get the diameter. Likely to be 22 mm, or, if imperial 21.5 mm.
2. I can understand you not wanting to disturb the parquet.
3. Do be aware that a new radiator is likely to have:
3a. A different distance between the entry points for the pipe. The distance will normally be that given for the radiator's length. If you go for a slightly shorter radiator than the existing, you can get extenders to match fairly closely the existing pipe centres. Don't go for the adjustable extenders, they often leak. If you get a longer radiator than the existing, you will need some fancy (but visible) pipework to connect, unless you go under the floor.
3b. A different distance for the centre's of the entry points from the wall. If you are replacing like for like this may not be much. You could probably get a couple of millimetres play in the existing pipes. Any more, and you will again need some altered pipework to math to the new centres.
4. You can get adaptors to go from 3/4" imperial pipe (the 3/4" refers to the nominal internal diameter of the pipe, not its outside diameter). E.g BES 6791. You would then need a 22 to 15 reducer to get to 15 mm pipe to the new radiator valves. The foregoing are solder connectors, as I don't think you have the room for compression couplings, and they might also look quite ugly.