Thanks all, I rather thought it would be a bad idea.
We've actually taken a bit of a punt and brought our booking for the RA Summer Exhibition forward one day to the 19th (which they were happy to do at no charge). That is still a national rail strike day, but hopefully the tubes & buses will be less awful (allowing that some commuters will be using them as alternatives to national rail).
Our original train booking on the 18th cannot be changed, so we've had to book another pair of singles for the day before. However, if the train we originally booked on ends up being cancelled then we'll get that one refunded. So fingers crossed the only additional cost will be one extra night in the Tottenham Hale Premier Inn (chosen because it's within walking distance of the wedding venue).
It also looks like there should be enough to keep us amused in the local area on the Friday, such as Walthamstow Marshes and the William Morris museum. So we can stroll about at leisure while feeling sorry for all the folks stuck in bus queues.
In reply to Bjartur i Sumarhus:
Cycling would have been an option for me but, unfortunately, definitely not for the missus.