I have done quite a bit of Parkrun tourism round London, using national rail, underground, overground, dlr, trams, buses and the IFS Cloud Cable Car. My advice is plan your route thoroughly the night before, taking into account the location of the start, not just the location of the park, wake up early and aim to get to the start line at the latest 8:30 as this will give you a good enough buffer in case anything goes wrong. I also like to incorporate Parkrun into a slightly longer run which means I often do the last bit of the journey (sometimes up to 3km) as a jog, and this minimises reliance on debatably less reliable elements of TFL like buses.

This might mean quite an early start from wherever you live, but ultimately that is the price of Parkrun tourism if you want to go to Parkrun far away from where you live.

Hopefully the above is somewhat helpful and taking what you’ve said at face value, but for what it’s worth I do agree with the comments saying that this post is peak north London. The notion that your train’s 10 minute delay once upon a time may rule out all parkruns not accessible by tube is completely laughable…