I'm glad you got that sorted out, NfkDumpling
Tesco slots (and Morrisons) can suddenly appear at any time of the day.
If you are not on their priority list, and don't manage to grab one of the midnight slots, you need to keep checking the site as often as you possibly can. Slots can appear randomly at any time. Sometimes you might strike lucky quite quickly and other times it will take several days at least.
Yesterday I decided that I needed to change the day of an existing slot (just shopping every two weeks isn't working out as well as I had hoped). I started monitoring the site early afternoon. Some unsuitable slots suddenly appeared around 6.30 and were gone in five minutes. Then this morning, at 7.45, some suddenly appeared for one of the days that I wanted, so I was able to grab one.
I had much the same experience on Morrison's site before my mum was on their priority list (except that the only slots we ever had access to then were for the following three days, not three weeks, which reduced even further our chances of getting one.
It can be very time-consuming and take a lot of persistence, but is doable!