They performed gamma ray spectroscopy but did not discover any strong signals, except for a very small spike at 803 keV. Some of the scientists were talking about the case and they were overheard by an older scientist who had worked on the UK's atomic weapons program back in the 50s. The early bombs relied on Po-210 and he recognized that 803 keV line as being characteristic of Po-210. Although the decay is almost exclusively via alpha particles, a very small fraction of decays happen via emission of a gamma ray at 803 keV.
Once they had the connection to Po-210 it was straightforward to test for its presence in his body.
I don't understand. So professionals from the AWE tried to identify the measured radiation lines from memory(?!), instead of consulting a publicly available database of spectral & decay lines? It's been a while since I've done any spectral analysis but I used to use ie.lbl.gov a lot (seems offline unfortunately) and they had a search function[0] that allowed you to filter their entire database of isotopes and decay chains by whatever line you were looking for.
[0]: https://web.archive.org/web/20150408041531/http://ie.lbl.gov...
https://www.argonelectronics.com/blog/litvinenko-and-the-per...
Also, from the article:
> The UK Health Protection Agency, which is advising authorities on technical aspects of the case, characterises the contamination in all 12 cases as “not significant enough to result in any illness in the short term,” while “any increased risk in the long term is likely to be very small.”
"An antistatic fan made by NRD, of Grand Island, N.Y., contains 31,500 microcuries of polonium 210 — or, in theory, more than 10 lethal doses."
Source: https://www.nytimes.com/2006/12/03/weekinreview/03broad.html
This was part of the reason why it took so long to discover the cause of Alexander Litvinenko's death by Polonium-210 poisoning. Doctors (and later detectives) had suspected some form of radiation poisoning, but the early tests used Geiger counters and came back negative. But Po-210 decays almost exclusively by emitting an alpha particle which is not detectable by Geiger counters. (And it also means it's not very dangerous outside the body but becomes extremely toxic if ingested.)