When you say plug is broken, I guess you mean the transformer? This provides a certain voltage to the charging control circuit within the vacuum cleaner. Look at the sticker on the transformer and it will give you the specific output needed by your machine. Just for example, it may say something like :
12V DC 2A with a symbol that identifies the polarity of the plug that attaches to the machine. Play close attention to the symbol after the voltage which will either be a straight line with dashes below (dc) or a straight line with a wavey line above (ac) Then go on ebay and search for wall adaptor charger and carefully match the sticker information and connector size with the photos of the various ones available on ebay. Will cost less than £5 and you'll be up and running again.
Another once-great name that had been bought by a retailer and is used to market cheap tat with little or no support.