In my book, Chinatown Kitchen - which is out now! -I detail basic ingredients that you can buy to build the basis of your cooking repertoire for Asian food. Here are my top 5, from right to left.
Chilli oil / sauce - Essential flavour enhancer for congee, soup, rice dishes, noodle dishes, grilled cheese sandwiches... The type of chilli oil or sauce alternates as I like to experiment with what I find in the supermarket. Stalwarts are Sriracha (the book actually has a home-made version of this too) and a classic oil made from just dried, ground chillis and Sichuan peppercorns.
Dark Soy Sauce - Usually used very sparingly, this adds colour and caramel-like flavour.
Light Soy Sauce - I prefer Pearl River Bridge Premium Deluxe - it is a little harder to find (See Woo definitely sell it) and a little more expensive than regular soy sauce, but it has a superior flavour that I love.
Chinkiang black vinegar - this is a very delicate, slightly sweet and fragrant Chinese vinegar. It's added at the end of cooking to preserve its flavour, and is used in sauces, soups and dipping sauces for dumplings.
Fish Sauce - I use 3 Crabs, upon the advice of the eminent Vietnamese guru, Uyen Leluu. It's flavoursome and fragrant, without the harsh saltiness you get from lesser brands. It's essential in Thai and Vietnamese cookery.
You can buy these in Asian supermarkets, and a lot of the ingredients are available in mainstream supermarkets like Waitrose, Sainsburys, Morrisons and Tescos. You can also buy online - Wai Yee Hong and Sous Chef deliver.