London England

Grocery stores, no problem. London is one of the largest metropolitan areas in the world. If you search the neighborhood you'll be lodging at on Google Earth, with the grocery store option enabled, you'll see the grocery stores. These will not be large suburban style food stores, of course--more like the kind of neighborhood grocery stores you would see in Paris or Manhattan.
Markets, depends on what kind of markets you mean.
You'll want to get a guidebook to London. Rick's will answer most of your questions.

Are you SURE you want to take a train from London to Portugal or Spain? Unless your destination is Barcelona, this will be a lengthy and not cheap endeavor; unless you're stopping off along the way to sightsee, you'll do much better to fly. From London, there are gazillions of flights to lots of cities in Spain and Portugal. For instance, if you want to see Andalucia, you can fly there nonstop, without having to stop in Madrid or Barcelona, unless you want to see them too.

To learn exactly what's involved in taking the train, use the rail guru The Man In Seat 61. Here's his Spain page: http://www.seat61.com/Spain.htm#.VcghxPmLjhA
and his Portugal page: http://www.seat61.com/Portugal.htm#.Vcgh_vmLjhA

To find flights, use Skyscanner: http://www.skyscanner.com/
Remember that London has 6 airports (according to the airlines) and some take more time and money to reach than others; consider this before buying. (If you save £10 on a ticket, but it costs you £20 more to get the airport and means you have to wake up at 4 AM to avoid missing your flight, that's not a bargain).

There is a nice Whole Foods in Kensington, big and with a hot food court. It's expensive, even by London standards. M&S there too, always a good bet for food.

There are no trains from London to Spain or Portugal.

The best you will be able to do will be Eurostar (St Pancras International station, all the way across London from Kensington) to Paris, then all the way across Paris to another station and another train to the Spanish border where the width between the rails changes, often with another change of train, and then more changes in Spain. There aren't a lot of rail connections between Spain and Portugal.

All this will take an age and cost a fortune.

Fly.

Pamela,

Last year, we stayed at the Holiday Inn Kensington and found it a fine launching pad for site-seeing. While it didn’t have the charm of a boutique hotel, we were traveling with a slightly mobility-challenged travel partner so the Holiday Inn was the perfect compromise. It’s located halfway between the Earl’s Court and Gloucester Rd tube stops (Earl’s Court has a lift) and is on the #7 bus line.

There is a Waitrose next door and a Tesco Superstore down the street. Best of all, there’s a huge Whole Foods Market up on Kensington High Street just steps from the High Street Kensington tune station.

Have a great trip.

Todd