Your statutory rights are, as you've suggested, are in respect of your contract with the retailer (rather than with the manufacturer, with whom you've never had a contract).
Within the first 6 months after purchase there's an automatic assumption in law (unless there's clear evidence to the contrary) that any fault that develops with an item must have come about through an 'inherent fault'. (i.e. something which was wrong at the time of purchase, such as a defective product or the poor use of materials or workmanship). The retailer is then obliged to repair or replace the item.
Thereafter the retailer continues to be obliged to repair or replace an item which has become defective due to an 'inherent fault' (usually for a period of up to 6 years) but it's up to the purchaser to show that the problem is related to an 'inherent fault'. Theoretically that might mean that you'd need to get an independent expert to certify that the most likely cause of the problem was such an inherent fault but, in practice, simply challenging the retailer to suggest any likely alternative might be all that's required.
So hassling Argos (and not taking 'No' for an answer) might do the trick.
A guarantee/warranty is completely separate to your statutory rights. It's a 'gift' from (in most cases) the manufacturer, rather than the retailer and can be as generous or as limited as the manufacturer (or retailer) chooses to make it. However Samsung UK provides a warranty on Galaxy Tab products lasting 24 months. So (if you get no joy from Argos) you should still be able to fall back upon the warranty provided by Samsung. Phone 0330 726 7864 to contact Samsung UK Support (Mon-Sat 0900-1800).