I too have the exact same problem (Minton tiled hallway), which is how i have come across your post (while searching for info..)
Some info that may be useful....
If you have Minton tiles, then Minton Hollins (the original maker) is now owned by H & R Johnson
www.johnson-tiles.com
I telephones them and said i was looking for some Minton tiles and they sent me an A4 card with 10 small tiles stuck to it and 7 different shapes (available in various sizes). They didn't charge for this and all the tiles i require are available off the shelf.
If your floor is anything like mine it is in very good condition in certain areas, and not so great in others. At various stages parts of it have been uncovered and covered and varnished to seal at different times.
I've tried loads of ways to clean various small parts (the out of the way bits, only a couple of inches square so if it went wrong i hadn't caused too much damage).
I've come to the conclusion that to have the floor restored profesionally is going to cost too much and so am going to live with some of the ageing affects (after all the floor is over 100 years old and so isn't new!).
I've decided to clean my floor in one go and then seal it all in one go. The best method i've come across is:
Use paint stripper for areas where it is varnished. Depending on the amount of varnish and tile condition some areas will take a single application, other two or three.
Work on around a metre squared at a time otherwise it is difficult to get the paint remover off at the right time.
Wash down the floor and then let it dry for a few days.
Pour on paint stripper liberally so the area is fully covered and is completely wet.
Rub the tiles vigorously with wire wool, make sure the paint stripper is kept moist and doesn't dry out. Add extra if the stripper goes tacky or dry.
You should lift quite a bit of varnish and dirt from the tiles if they're like mine, and after around 5-10 mins scrubbing the tiles should be quite a bit cleaner and the paint stripper has gone tacky (but not dry).
Then i found the best way to get this whole lot of goo off the floor was to use Cif to cut into it. Squirt Cif (or any other cream cooker type cleaner) onto the floor so it is wet and using more wire wool rub it around. Add hot water to the floor a little bit as you do this to dilute and make the floor nice and wet.
If you use this method the Cif mixes with the paint remover and you can then wipe off the floor with hot soapy water. If you use just water it can smear, and white spirit can be a bit hit and miss.
Once done give the section a real good clean with more hot soapy water (i use those small sponges with a rough back at this stage). Then wash down with a cloth and hot soapy water. Lastly give a real good mop with just hot water.
The whole procedure takes around 20 minutes from adding the paint stripper to finishing washing down. This doesn't make the tiles as new, but i reckon when i've done my whole floor it will look pretty good.
I experimented with putting paint stripper on, leaving for 5-10 mins then going back and adding the same again, leaving for 5-10 mins and then starting cleaning. This used twice as much paint stripper and brought up the tiles very well, but it also made them look considerably newer.
If i could reproduce this across the whole floor then it really would look good, but i don't think i could do it consistantly (i'm a novice after all - i presume the pros could though).
So rather than aim for an old floor that looks heavily restored (badly in parts with a patchy finish) i'm going for an old floor that looks old but well cleaned and maintained (a sympathetic restoration i think they call it...).
After all if i wanted a sanatised perfect floor i'd just rip it up and start again or carpet it (which thankfully the previous owners did for 40 years helping to keep it in decent nick
.
Incidentally, one last thing that i found worked to a degree is an acidic cleaner (the type to clean outside flag stones).
With this i worked with it neat (add lots so it doesn't dry out) and worked in with a foam mop soaked in water, and then left for a few minutes, and mopped off with hot soapy water. I didn't want to leave on as it tends to evaporate.
It took a few goes to get any real affect (i didn't want to soak the floor too much or leave on for too long as it reacted slightly with the grout between the tiles even though i can't really see any).
But it did act like i suppose a fine sandpaper would on wood and just helped to blend the different areas i'd done together.
Then to finish it seems applying a varnish with a cloth very lightly (multiple layers) once the floor is 100% dry is the best way to seal. I haven't experimented too much as each layer i add will have to be removed when i come to do the whole floor.
For what it is worth though i have found 3 layers of matt varnish applied with a cloth in a circular motion in very thin layers gives the look i require. If my floor was 100% perfect and a big country house and i wanted a posh look i'd probably would go for gloss. But it isn't, instead the floor was installed in an 1890's victorian house to provide a hard wearing floor which at the time was probably quite reasonable in price.
I found matt keeps the tiles looking old, natural and faithful to what i want to achieve, but i can see how a gloss Minton floor could look very eye catching.
I've done various sections of my floor and i know that the above way isn't the 'proper' way, but i know how difficult it is to find useful info on the net and so thought i'd share. I don't know if your tiles are the same as mine or in the same condition, so if you're going to try any of the above make sure you only test very small patches in areas that won't be seen until your confident you have got it right for your situation.
I'm off to continue my search on laying minton floor tiles, any tips you come across please post as i'm still at the trial and error stage myself !