Cheryl, call me Pete, we are Pete and Gina, we are in Essex also...
don't go to Picadilly itself, as you wont find the ingredients there, take the Blue line, the Picadilly line, it should get you to Earls court station, or you can always drive there, or get your partner to drive you there, there is limited parking in Hogarth Place, its metered, its about 40p per 20 minutes or something like that.
Just remember, if you go in the weekday, the supermarkets there are in the Transport for London congestion zone, there is a fee of £8.00 to pay for entry, Hogarth Place is just inside the zone by about 5 meters, Earls court road is not in the zone, using the Tube and buses is cheaper than taking a car, but a car is more convenient.
You can also buy Oiishi, Datu Puti, anything you want really, Cuttle Fish, Milk Fish, Banggus, lots of different kind of Fish you are used to, you can buy Thai Fragrant rice which is better rice than Tescos, or the other markets in town where you live.
You need a day out really, to go up there, best of luck with it. let us know how it goes.