First thing I'd do is check the Motorised valve for the Hot Water circuit is opening as it should, that may be your issue, rather than a problem with the cylinder and/or a blockage.
Secondly, sort those cisterns out if you're keeping it open vented. Needs a proper base/platform, remove that dead leg of the old feed to the F&E cistern, (the small cistern could be removed altogether now, its not serving any purpose), and reconnect the overflow from the Cold Storage cistern, so it wont leak water everywhere if a problem arises.
If you're going along the Unvented route, the lot will be redundant, if you're keeping the current open vented setup, then I'd replace the cistern with a modern version with sealed lid etc.