IIRC, Tesco has no pre-made sandwiches that don't include mayonnaise.
Sainsbury's has almost no mayonnaise-free sandwiches, but I forgive them because they have delicious and cheap scones with cream and strawberry jam, apple turnovers, etc.
Marks & Spencer is where it's at for no-mayonnaise pre-made sandwiches: the scrumptious Wensleydale cheese and caramelised carrot chutney, the British ham and cheddar, the salmon and soft cheese...
And they have great (albeit expensive) smoothies and juice drinks, like their strawberry-vanilla yogurt smoothie and their pressed apple with mango juice.
Mmm...