The ABP website is only good as a guide. The ships on passage page only updates every hour, and is not always reliable at doing that. It does give any vessel on passage's last reported position, but if you add any delays in that to the hour delay updating it can give a position a couple of hours out. if you don't have AIS, and you have to leave home quite a while before the ships are due, the best estimate for inward traffic is to look at the planned voyages page. That the upriver vessels and add approx. 3 hours to give a time at Burton or Swinefleet. For example tonight the page gives Paper Star and Bienville due to leave Bull Anchorage for Goole at 2214, add three hours and you will need to be at Swinefleet no later that 0100 if you want to catch them. Sailing vessels are a bit easier, you need to be in position 1 hour before high water, which is almost the same time as the inward vessels at Burton and Swinefleet.
Sailings are often cancelled due to all sorts of reasons, but it's very unusual to have nothing moving on a tide.
If possible use ABP's site to see what is likely to be moving inwards, then monitor an AIS site like Martine Traffic. When you see the vessels start to move or pass Spurn, you've approx. 3 hours to get into position, which you could probably manage comfortably from South Yorkshire.