You probably need to sharpen your pencil and terminology a little.
There are no group A or LSA aircraft at the moment so that suggests a little vagueness or lack of knowledge.
It can be done. The Scottish Aero Club have just bought a Eurostar which is virtually the aircraft you are describing. Under £100 per hour for instruction (just!) and £3k for a twentieth share. Pretty attractive numbers. A non-equity group would be more expensive but should n't be a lot more otherwise the old tin will take your trade.