Nope. Tax will be £140. Its done on the vehicle's (mini's) original specification. Due to the age of a classic mini it is either up to 1549cc or over 1549cc.
Sub frame would be a complete custom job or you could use something like a bare suzuki frame from all speed (about £375). Including the range rover mounts, box section and plate steel needed you should be able to build a frame and brace bars (if needed) for under £100 (probably even less). Its the drive shafts that are the pain in the back side to do and you will end up spending a bit of money on getting done.
From the pictures above the aygo frame doesn't look to be much use.
First thing I would do before committing to buying anything is to get a tape measure and measure everything up. Sounds obvious but a lot of people ask 'will this engine fit in a mini?' and don't bother to do this.
Going on experience after building my own Vauxhall set up, its not worth it in my mind. For the work involved I wouldn't do an engine conversion for less that 100 bhp. The micra 1.3 conversion is only just worth it in my mind.
A rebuilt 1275 is probably going to cost you about the same if not less, will be a lot less work, will give you the same kind of fuel efficiency and will be more powerful.