The busyness is usually due to two trains departing around the same time (within half an hour of each other).
It says on your ticket what time you should arrive at St P (the ones I've seen recently have said 75 mins before departure, although I have also known them contact me the day before suggesting I arrive sooner, as if that weren't too late for me to change my connecting trains!).
I worry more about my English train being delayed rather than the Eurostar queues being too long - I've seen the queue start right back by the main doors to St Pancras and still got through with time to spare.
If you arrive any earlier than 90 mins before your train they don't let you join the queue anyway!!!
If you get there late for any reason, speak to staff, they will let you jump the queue. I've never had to do this myself, but I have seen people do it.
It is also possible to buy a CIV ticket to London International (you need to ask for this at the station when you buy the ticket and you cannot buy it online (or you can, but you need to know how!)). This gives you international conditions of travel, so you can travel on the next service if you miss the train you are booked on. I suspect they would let you do this anyway, if there was a seat, but CIV guarantees it. I always have an onward European train booked, so really don't want to miss my Eurostar so I'm always very conservative about the train I book to London.
And PPs are correct, everyone joins the same queues so hand bag only will make no difference.