We used our Phil&Teds Sport buggy for our first two kids, and it got rather filthy in the process, and now there is the third one on the way! What is the best way to wash the buggy? The fabric parts don't seem to be detachable by design...
I am not familiar with this type of stroller, or, "buggy" as you call it, but a google search quickly brought me to the manufacturer's website where I found a "support" link. Here, you can search for your specific product's washing instructions (in case there are special considerations based on fabric type, etc). I'm my experience it is never apparent how to get the fabric off- you must consult the user manual, which I imagine is long gone. The website should have a downloadable version for you as long as you know the model #.
However, if you want some non- product specific advice from a mother of three boys it is this: hose it down. Choose a nice, warm, dry spell (it takes a few days to dry depending on the fabric). I used to fill a small bucket with a few drops of dish soap and warm water and then use a rag to gently spot clean the really nasty stains before the general hosing. I suggest doing this on a hard surface, such as asphalt, concrete, or the like so you don't get it even dirtier in a mud puddle (I made this mistake once- you don't need to make it also.) I would then wipe down the frame and soak up as much water as I could with some towels. If you don't have agreeable weather for a hosing, the spot clean alone should do the trick.
I used to focus on the straps-they tend to get the dirtiest, and kids can get them in their mouth, so they need to be petrified-jelly free.
UPDATE I recently started using oxygen bleach on my stroller straps because dishsoap was no longer adequate. I spray it on then lightly agitate with an old toothbrush. You can purchase it, or, you can make your own: in a plastic spray bottle mix 1/2 cup of baking soda with 1 cup of warm distilled water (you don't want any minerals contaminating your formula), shake to dissolve, than add 1/2 cup of 3% hydrogen peroxide (the kind you use for first aid). I'm sorry, I don't know how to convert this to metric measurements. Please do a test to determine colorfastness before you start spraying this all over your stroller. It will need a rinse when you are done.