Check Eurostar site FAQS for definitive answer
The official rule says: You need to carry and lift your bags safely on your own. But I think this should be true - otherwise how would you get them to the train station? *g*
The official answer you'll get: You may carry 2 x pieces of luggage up to 85cm long and 1 x hand luggage e.g. handbag, laptop bag or briefcase.
I did the journey this week with a lot of luggage and in fact I can't imagine that anyone will enforce this rule if it's more. But that's unofficial and you may never know...
Would you like to carry much more?
Currently in Brussels E* lounge. Many have large backpack and mid sized wheeled suitcase.
Leaving on €* from LON a week or 2 ago (and on a pass, end of 1st trip on the half price 3-month and just avoiding the strikes in GB) there were indeed it seems more enforcements that 2 (but very big) cases/rucksacks would be the max. But at that particualr time+train there were quite many people struggling with such heaps-I travel light amap, also then.
The airport-imitation luggage check seems to let anyone just pass by-no idea (except the very obvious) to what these searches are meant for.
And was in HD just the week before that-on the 9€ cheap travel ticket