Peel the lemons with a vegetable peeler, then cut the rind into fine shreds and set aside. Squeeze the juice into a bowl. Reserve the pips, then roughly chop the lemon shells.
Peel one quarter of the quinces, halve and core. Cut the flesh into thin strips and add to the lemon juice so that they don't discolour. Add the quince peelings, core and quince seeds to a preserving pan. Roughly chop the remaining unpeeled quinces, add to the preserving pan with the lemon shells and reserved pips.
Add 1 litre (1¾ pints) water to the preserving pan, cover and cook gently for 30 minutes or until the quinces are soft. Pour through a jelly bag suspended over a bowl and leave to drip for 30 minutes or until cool enough to squeeze the bag to extract as much juice as possible. You should have about 600 ml (1 pint) of juice. Meanwhile, add the lemon rind, sliced quince, lemon juice and remaining water to a small saucepan and cook, covered, for 20 minutes, until just tender.
Pour the squeezed quince juice back into the preserving pan, add the lemon rind, sliced quince and cooking water. Pour in the sugar and heat gently, stirring from time to time, until dissolved. Increase the heat and boil rapidly until setting point is reached (10–20 minutes).
Skim with a draining spoon or stir in butter if needed. Leave to stand for 10 minutes, then ladle into warm, dry jars, filling to the very top. Cover with screw-top lids, or with waxed discs and cellophane tops secured with elastic bands. Label and leave to cool.