For some reason, no source can outright agree with the number of episodes of Top Gear. One look at IMDb will give you 184 featuring Clarkson, and 199 featuring Hammond. However, lists on that site include the various compilations made over the years, and the episode count isn't actually as high as the latter figure would imply.
The first 9 series are easy, as the two specials which had aired by that point (Olympics and US), were regular episodes. The problems only start with the Polar Special, which came out afterwards.
Wikipedia, for whatever reason, does not recognise the Polar Special as an episode, despite airing on TV in between S9 and S10. As a result, I consider it to be the 81st episode, with Series 10, Episode 1 being the 82nd episode. This is the first point of divergence.
The next point of divergence happens all the way at the end of Series 18, following the show's 147th episode (146th on Wikipedia), which is the Bond Car special presented by Richard Hammond. Again, despite being a full-length episode of the show which aired in-between S18 and S19, it is ignored by Wikipedia. As a result this is now the 148th episode, with Series 19, Episode 1 being the 149th.
The next point of interest concerns something I wasn't even aware existed until a few weeks ago - the Sydney Festival with Clarkson, May and Pizzati/Jacobson from the Australian show. It aired 22 days after Series 20 concluded, and on BBC Knowledge rather than BBC 2. No source I can find lists this as a Top Gear episode, in spite of the fact it's full-length and contains new footage with two of the presenters. As a result I now refer to this as the 162nd episode of the show, with Series 21 being episodes 163 through 169, rather than 160 through 166, as they're considered on Wikipedia.
After Series 21, we get the first series of James May's Cars of the People, which is branded as a "Top Gear Special" everywhere except the UK, including the DVD releases. They also feature the Top Gear "cog" logo and were 60 minutes long, airing in the exact same timeslot as a normal episode of Top Gear. As the Bond Car special featured just Hammond and yet is included in the total count, I've included all 6 of these as well. So Series 1 of COTP is considered as episodes 170 through 172.
Then we have Series 22, preceded by the two-part Patagonia Special which form episodes 173 and 174. A week before the series premiered, we got a live special known as "An Evening With Top Gear", which featured the trio talking about the upcoming series alongside clips. Normally, something like this would be a compilation, but instead, as it occurred prior to the series, I consider it an episode outright, especially since it was 60 minutes long and featured the show's title sequence. This is episode 175.
Finally, we have Series 22, which is now episodes 176 through 183, rather than 169 through 176, as they're listed on Wikipedia. We've practically added a whole series' worth of episodes on by this point, and that's before we add the final 3 episodes of May's series, taking the count of CHM-era Top Gear to a final total of 186.
However, that said, I then consider Series 23, Episode 1 as the next episode chronologically, #187, and do not include the two A-Z specials released in-between, as these were solely clip shows that were, in my opinion, no different from "The Best Of British" or "Top 41" compilation specials.
Further confusion is abound when it turns out the direct-to-video releases (e.g. Uncovered, Apocalypse) were aired on TV in the US, however, as they were aired out of sequence and never made it to TV in the UK, these are not counted.