Had someone pull out in front of me and hit my clutch a bit hard, broke the piece of plastic you can see in the pictures, had to spin it round to get a picture of the broken area. Problem now is that the pedal goes down too far and the broken part gets stuck inside the.. bit it goes into (don't know names for things sorry). Is this easily fixed? Garage quoted me £200, that made me sad. 

Looks like it's the clutch master cylinder I'd go and get a couple of quotes from independent garages as £200 sounds a bit expensive 

 

hard to tell from pics what the access is like to work on it. Could you possibly put a small worm drive hose clip around the part where it broke and do it up tight? as far as I can tell from what you say and the pics that might do the job if you can get it to firmly stay in place.  or may be also adding a load of araldite around the sides of the hose clip to maybe make it even less likely to slide.

Or get a washer with same internal diameter as the shaft that goes into the master cylinder and a much larger external diameter (sometimes called penny washers). saw a slit from the outside to the centre hole. bend the slit open with pliers. put over the shaft (between the broken part and the master cyinder) and then close it back up with pliers. I appreciate this can be a bit fiddly particularly with restricted access. 

or the proper way would seem to be a brand hew clutch master cylinder. They do not cost much but of course the fitting and bleeding adds cost if you can not do it yourself.

if this was mine I would most likely do it with the washer,  and glue (araldite) the washer up against the raised shoulder where the piece broke off

(yes, I know everyone will say I am bodging it)

I'm with isetta - if it is just a case of the shoulder now going inside the neck of the cylindrical bit, a big rubber washer / o-ring, cut then reglued should sort it out at least temporarily. Make sure that you ensure full un-impeded operation of your clutch pedal afterwards.

I never thought they'd use plastic parts on a clutch... wow!

£200 is not a bad price, my clutch did the same thing and I replaced mine myself but it's a ***** to get to and the master cylinder itself is about £70. The new ones are better though as they are metal and plastic not just plastic.

Just had mine done £174-00 for a 2013 Ford Focus. Who designed this should be shot with summick very smelly and sticky unless it was fords plan to screw some more money out of their customers, is there no recall or compensation