I can only talk for England and Wales, as Scotland and Northern Ireland have a seperate legal system. The same and fitting by a business of mod chips is illegal (notice I said business), they can be purchased from outside E&W and fitted privately. Selling a modded console is also illegal, which is why places like cash converters/generators, etc removed all notices saying whether a console was chipped when the law changed.
We also do not have the legal right to back something up, though no one has been prosecuted if it is for personal use, I think because it would be impossible to get an impartial jury and the companies won't waste their money on such a suit as it is civil law. Though having to break encryption is illegal under criminal law and does carry the risk of being prosecuted. Though this is a hard law to use against an individual who has done it for personal use, after all how will they know?
I know it sounds bad, but no noe has ever been prosecuted for modding their own consoles or backing anything up yet. Only those that have sold them commercially or with copied games on the hdd of those consoles that have them have been delt with under the law.