As people have already mentioned, much is about your personal risk appetite and potential consequences.

A few things to consider are:
1) Delay/cancellation on LAX-OAK and alternative means of reaching OAK in time
2) Luggage. If you have checked baggage, your risk may be bigger due to the time it takes to retrieve them and recheck
3) Consequences of missing the OAK-LGW. You may have commitments immediately upon landing at LGW, or you may have a few days with no commitment, in which case you might not be too worried about it in that respect
4) Affordability of alternative flights if you miss OAK-LGW. If you happen to have a (admittedly somewhat unusual, so check the fine print) travel insurance that covers you for 'self-transfer that resulted in a missed flight" to the full cost of a replacement flight (a lot of policies only cover a small amount for this), then you might feel fine, as long as you have allowed sufficient time for the insurers to deem reasonable.

Basically, if you happen to be on a fully flexible ticket and you see lots of availability on the next OAK-LGW (therefore you can just ask to be rebooked the next day, for instance) and you have no commitments that you need to meet the next day for instance, then you could be brave about things because it might be of no consequence to you.

However, if you find that the alternative flights are now very expensive, your travel insurance does not cover the consequence fully, and you have to get back to work immediately etc., then you'd want to work on minimising your risk because there are too many consequences.