Seems to be legit. Will be trying it with a bill soon.
Having spent some time investigating, it seems that some of us are genuinely entitled to use this. You need an old surname. It was quite easy for me as I have a rare surname (only 72k in the UK). There are three branches of my family. One from London, one from Ireland and one from America. The London strain were around 300 years prior to the event with both birth and death certificates to back this. I am not from this group (and thankfully not a yank either) so my claim would be fraudulent.
However, yours may not be. If you have family from London prior to the great fire, you have a plausible claim and then becomes the authority’s problem to prove you are not.