Stanner - you say "they are in a pretty bad state". What do you mean? You also seem to suggest that you have lifted them - have you, or do you have to do this?
Assume they're up - they may be 'clagged' up with sand/cement residue; this can be easily removed with Mortar Cleaner, a transparent liquid (16% diluted hydrochloroic acid) which is designed for this type of purpose. We get 5L containers from Travis Perkins. We also use it to 're-vitalise' period bathroom china, it's brilliant stuff with plenty of uses (I even use it to de-scale my kettle at home!!). Care needs to be taken when using the stuff, vinyl gloves, safety specs, old clothes and plenty of water to neutralise the acid (keep it away from stainless steel).
Very old quarry tile tended to have a plain reverse face, so if you have any with a damaged front face it might be possible to flip them. Replacements will be difficult to obtain (unless you have a decent reclamation yard near to you), so another dodge is to use modern (unglazed) tiles which will need to be reduced in size ('cos they're metric so won't match the imperials) using an angle grinder or, better still a diamond wheel tile cutter - get a cheap one from a DIY shed.
My guess is that your tiles might be unglazed terra-cotta, so when the floor is finished it'll need to be 'sealed' - we use linseed oil.