Your car would not be on a Hoegh vessel - they don't transport Teslas to the UK, so no surprise there.
I've just checked all the ships due to arrive into Southampton between 01 Sep and 5 Sep and there is nothing there that has caught my eye. Which again is no surprise because I monitor all departures from Shanghai and I have no likely suspects in the timeframe.
This is unusual, any other quarter I would expect to see a ship with about 4500 cars pitch up around 15 -20 Sep, however nothing left Shanghai as far as I can tell, at least routing direct to Southampton. I mentioned before there is a remote possibility that NEPTUNE HORIZON may have some cars left onboard for Southampton after she unloads in Koper, but that is a bit of a stretch if only because we don't even know whether she has any Teslas onboard in the first place! There was talk of some cars heading for Glasgow that were unloaded in Dublin. Again, this is very unusual and I would dread to see the paperwork involved for that to happen and in any case I think it unlikely.
If you have your VIN you can DM it to me and I may be able to delve a little deeper. In the meantime you can stick it in
HERE to get an approximation of the build date. If the build date looks like it was earlier than 14 Jul, you can assume it has already arrived in Southampton. If later, I would be very interested.